diff --git a/binaries/data/config/default.cfg b/binaries/data/config/default.cfg
index b49da8636c..b67a3a645e 100644
--- a/binaries/data/config/default.cfg
+++ b/binaries/data/config/default.cfg
@@ -486,6 +486,8 @@ name_id = "0ad"
 duplicateplayernames = false      ; Rename joining player to "User (2)" if "User" is already connected, otherwise prohibit join.
 lateobservers = everyone          ; Allow observers to join the game after it started. Possible values: everyone, buddies, disabled.
 observerlimit = 8                 ; Prevent further observer joins in running games if this limit is reached
+observermaxlag = 10               ; Make clients wait for observers if they lag more than X turns behind. -1 means "never wait for observers".
+autocatchup = true        ; Auto-accelerate the sim rate if lagging behind (as an observer).
 
 [overlay]
 fps = "false"                     ; Show frames per second in top right corner
diff --git a/binaries/data/mods/public/gui/options/options.json b/binaries/data/mods/public/gui/options/options.json
index eccaca9747..ce7c494d46 100644
--- a/binaries/data/mods/public/gui/options/options.json
+++ b/binaries/data/mods/public/gui/options/options.json
@@ -27,12 +27,6 @@
 				"tooltip": "If you disable it, the welcome screen will still appear once, each time a new version is available. You can always launch it from the main menu.",
 				"config": "gui.splashscreen.enable"
 			},
-			{
-				"type": "boolean",
-				"label": "Network warnings",
-				"tooltip": "Show which player has a bad connection in multiplayer games.",
-				"config": "overlay.netwarnings"
-			},
 			{
 				"type": "boolean",
 				"label": "FPS overlay",
@@ -57,25 +51,6 @@
 				"tooltip": "Always show the remaining ceasefire time.",
 				"config": "gui.session.ceasefirecounter"
 			},
-			{
-				"type": "dropdown",
-				"label": "Late observer joins",
-				"tooltip": "Allow everybody or buddies only to join the game as observer after it started.",
-				"config": "network.lateobservers",
-				"list": [
-					{ "value": "everyone", "label": "Everyone" },
-					{ "value": "buddies", "label": "Buddies" },
-					{ "value": "disabled", "label": "Disabled" }
-				]
-			},
-			{
-				"type": "number",
-				"label": "Observer limit",
-				"tooltip": "Prevent further observers from joining if the limit is reached.",
-				"config": "network.observerlimit",
-				"min": 0,
-				"max": 32
-			},
 			{
 				"type": "boolean",
 				"label": "Chat timestamp",
@@ -425,7 +400,7 @@
 		]
 	},
 	{
-		"label": "Lobby",
+		"label": "Networking / Lobby",
 		"tooltip": "These settings only affect the multiplayer.",
 		"options":
 		[
@@ -447,6 +422,45 @@
 				"label": "Game rating column",
 				"tooltip": "Show the average rating of the participating players in a column of the gamelist.",
 				"config": "lobby.columns.gamerating"
+			},
+			{
+				"type": "boolean",
+				"label": "Network warnings",
+				"tooltip": "Show which player has a bad connection in multiplayer games.",
+				"config": "overlay.netwarnings"
+			},
+			{
+				"type": "dropdown",
+				"label": "Late observer joins",
+				"tooltip": "Allow everybody or buddies only to join the game as observer after it started.",
+				"config": "network.lateobservers",
+				"list": [
+					{ "value": "everyone", "label": "Everyone" },
+					{ "value": "buddies", "label": "Buddies" },
+					{ "value": "disabled", "label": "Disabled" }
+				]
+			},
+			{
+				"type": "number",
+				"label": "Observer limit",
+				"tooltip": "Prevent further observers from joining if the limit is reached.",
+				"config": "network.observerlimit",
+				"min": 0,
+				"max": 32
+			},
+			{
+				"type": "number",
+				"label": "Max lag for observers",
+				"tooltip": "When hosting, pause the game if observers are lagging more than this many turns. If set to -1, observers are ignored.",
+				"config": "network.observermaxlag",
+				"min": -1,
+				"max": 10000
+			},
+			{
+				"type": "boolean",
+				"label": "(Observer) Speed up when lagging.",
+				"tooltip": "When observing a game, automatically speed up if you start lagging, to catch up with the live match.",
+				"config": "network.autocatchup"
 			}
 		]
 	},
diff --git a/binaries/data/mods/public/gui/session/NetworkDelayOverlay.js b/binaries/data/mods/public/gui/session/NetworkDelayOverlay.js
new file mode 100644
index 0000000000..a687c8d204
--- /dev/null
+++ b/binaries/data/mods/public/gui/session/NetworkDelayOverlay.js
@@ -0,0 +1,63 @@
+/**
+ * Shows an overlay if the game is lagging behind the net server.
+ */
+class NetworkDelayOverlay
+{
+	constructor()
+	{
+		this.netDelayOverlay = Engine.GetGUIObjectByName("netDelayOverlay");
+
+		this.netDelayOverlay.caption="toto";
+		this.caption = translate(this.Caption);
+		this.sprintfData = {};
+
+		this.initialSimRate = Engine.GetSimRate();
+		this.currentSimRate = this.initialSimRate;
+
+		setTimeout(() => this.CheckDelay(), 1000);
+	}
+
+	CheckDelay()
+	{
+		setTimeout(() => this.CheckDelay(), 1000);
+		let delay = +(Engine.HasNetClient() && Engine.GetPendingTurns());
+
+		if (g_IsObserver && Engine.ConfigDB_GetValue("user", "network.autocatchup"))
+		{
+			if (delay > this.MAX_LIVE_DELAY && this.currentSimRate <= this.initialSimRate)
+			{
+				this.currentSimRate = this.initialSimRate * 1.1;
+				Engine.SetSimRate(this.currentSimRate);
+			}
+			else if (delay <= this.NORMAL_DELAY && this.currentSimRate > this.initialSimRate)
+			{
+				this.currentSimRate = this.initialSimRate;
+				Engine.SetSimRate(this.currentSimRate);
+			}
+		}
+
+		if (delay < this.MAX_LIVE_DELAY)
+		{
+			this.netDelayOverlay.hidden = true;
+			return;
+		}
+		this.netDelayOverlay.hidden = false;
+		this.sprintfData.delay = (delay / this.TURNS_PER_SECOND);
+		this.sprintfData.delay = this.sprintfData.delay.toFixed(this.sprintfData.delay < 5 ? 1 : 0);
+		this.netDelayOverlay.caption = sprintf(this.caption, this.sprintfData);
+	}
+}
+
+/**
+ * Because of command delay, we can still be several turns behind the 'ready' turn and not
+ * particularly late. This should be kept in sync with the command delay.
+ */
+NetworkDelayOverlay.prototype.NORMAL_DELAY = 3;
+NetworkDelayOverlay.prototype.MAX_LIVE_DELAY = 6;
+
+/**
+ * This needs to be kept in sync with the turn length.
+ */
+NetworkDelayOverlay.prototype.TURNS_PER_SECOND = 5;
+
+NetworkDelayOverlay.prototype.Caption = translate("Delay to live stream: %(delay)ss");
diff --git a/binaries/data/mods/public/gui/session/NetworkDelayOverlay.xml b/binaries/data/mods/public/gui/session/NetworkDelayOverlay.xml
new file mode 100644
index 0000000000..7992d99773
--- /dev/null
+++ b/binaries/data/mods/public/gui/session/NetworkDelayOverlay.xml
@@ -0,0 +1,14 @@
+<?xml version="1.0" encoding="utf-8"?>
+<!-- Put this under the regular gamestateNotifications. -->
+<object name="netDelayOverlay"
+	type="text"
+	hidden="false"
+	ghost="true"
+	z="199"
+	size="100%-300 60 100%-110 80"
+	font="mono-10"
+	textcolor="white"
+	text_align="right"
+	text_valign="top"
+	sprite="color: 0 0 0 100"
+	/>
diff --git a/binaries/data/mods/public/gui/session/session.js b/binaries/data/mods/public/gui/session/session.js
index 6ef89db5a0..890bcbfc8c 100644
--- a/binaries/data/mods/public/gui/session/session.js
+++ b/binaries/data/mods/public/gui/session/session.js
@@ -20,6 +20,7 @@ var g_GameSpeedControl;
 var g_Menu;
 var g_MiniMapPanel;
 var g_NetworkStatusOverlay;
+var g_NetworkDelayOverlay;
 var g_ObjectivesDialog;
 var g_OutOfSyncNetwork;
 var g_OutOfSyncReplay;
@@ -289,6 +290,7 @@ function init(initData, hotloadData)
 	g_Menu = new Menu(g_PauseControl, g_PlayerViewControl, g_Chat);
 	g_MiniMapPanel = new MiniMapPanel(g_PlayerViewControl, g_DiplomacyColors, g_WorkerTypes);
 	g_NetworkStatusOverlay = new NetworkStatusOverlay();
+	g_NetworkDelayOverlay = new NetworkDelayOverlay();
 	g_ObjectivesDialog = new ObjectivesDialog(g_PlayerViewControl, mapCache);
 	g_OutOfSyncNetwork = new OutOfSyncNetwork();
 	g_OutOfSyncReplay = new OutOfSyncReplay();
diff --git a/binaries/data/mods/public/gui/session/session.xml b/binaries/data/mods/public/gui/session/session.xml
index 723b3c7b4f..4cdaef004b 100644
--- a/binaries/data/mods/public/gui/session/session.xml
+++ b/binaries/data/mods/public/gui/session/session.xml
@@ -38,6 +38,7 @@
 	<include directory="gui/session/hotkeys/"/>
 
 	<include file="gui/session/NetworkStatusOverlay.xml"/>
+	<include file="gui/session/NetworkDelayOverlay.xml"/>
 	<include file="gui/session/PauseOverlay.xml"/>
 	<include file="gui/session/TimeNotificationOverlay.xml"/>
 
diff --git a/source/network/NetServer.cpp b/source/network/NetServer.cpp
index 8f4114a6bf..2674c88219 100644
--- a/source/network/NetServer.cpp
+++ b/source/network/NetServer.cpp
@@ -747,7 +747,7 @@ void CNetServerWorker::OnUserLeave(CNetServerSession* session)
 	RemovePlayer(session->GetGUID());
 
 	if (m_ServerTurnManager && session->GetCurrState() != NSS_JOIN_SYNCING)
-		m_ServerTurnManager->UninitialiseClient(session->GetHostID()); // TODO: only for non-observers
+		m_ServerTurnManager->UninitialiseClient(session->GetHostID());
 
 	// TODO: ought to switch the player controlled by that client
 	// back to AI control, or something?
@@ -1402,7 +1402,9 @@ bool CNetServerWorker::OnJoinSyncingLoadedGame(void* context, CFsmEvent* event)
 	}
 
 	// Tell the turn manager to expect commands from this new client
-	server.m_ServerTurnManager->InitialiseClient(session->GetHostID(), readyTurn);
+	// Special case: the controller shouldn't be treated as an observer in any case.
+	bool isObserver = server.m_PlayerAssignments[session->GetGUID()].m_PlayerID == -1 && server.m_ControllerGUID != session->GetGUID();
+	server.m_ServerTurnManager->InitialiseClient(session->GetHostID(), readyTurn, isObserver);
 
 	// Tell the client that everything has finished loading and it should start now
 	CLoadedGameMessage loaded;
@@ -1530,7 +1532,11 @@ void CNetServerWorker::StartGame(const CStr& initAttribs)
 	m_ServerTurnManager = new CNetServerTurnManager(*this);
 
 	for (CNetServerSession* session : m_Sessions)
-		m_ServerTurnManager->InitialiseClient(session->GetHostID(), 0); // TODO: only for non-observers
+	{
+		// Special case: the controller shouldn't be treated as an observer in any case.
+		bool isObserver = m_PlayerAssignments[session->GetGUID()].m_PlayerID == -1 && m_ControllerGUID != session->GetGUID();
+		m_ServerTurnManager->InitialiseClient(session->GetHostID(), 0, isObserver);
+	}
 
 	m_State = SERVER_STATE_LOADING;
 
diff --git a/source/network/NetServerTurnManager.cpp b/source/network/NetServerTurnManager.cpp
index 567fcd4e43..fa2de8260e 100644
--- a/source/network/NetServerTurnManager.cpp
+++ b/source/network/NetServerTurnManager.cpp
@@ -24,6 +24,7 @@
 
 #include "lib/utf8.h"
 #include "ps/CLogger.h"
+#include "ps/ConfigDB.h"
 #include "simulation2/system/TurnManager.h"
 
 #if 0
@@ -73,9 +74,17 @@ void CNetServerTurnManager::NotifyFinishedClientCommands(CNetServerSession& sess
 
 void CNetServerTurnManager::CheckClientsReady()
 {
+	int max_observer_lag = -1;
+	CFG_GET_VAL("network.observermaxlag", max_observer_lag);
+	// Clamp to 0-10000 turns, below/above that is no limit.
+	max_observer_lag = max_observer_lag < 0 ? -1 : max_observer_lag > 10000 ? -1 : max_observer_lag;
+
 	// See if all clients (including self) are ready for a new turn
 	for (const std::pair<const int, u32>& clientReady : m_ClientsReady)
 	{
+		// Observers are allowed to lag more than regular clients.
+		if (m_ClientsObserver[clientReady.first] && (max_observer_lag == -1 || clientReady.second > m_ReadyTurn - max_observer_lag))
+			continue;
 		NETSERVERTURN_LOG("  %d: %d <=? %d\n", clientReady.first, clientReady.second, m_ReadyTurn);
 		if (clientReady.second <= m_ReadyTurn)
 			return; // wasn't ready for m_ReadyTurn+1
@@ -171,13 +180,14 @@ void CNetServerTurnManager::NotifyFinishedClientUpdate(CNetServerSession& sessio
 	m_ClientStateHashes.erase(m_ClientStateHashes.begin(), m_ClientStateHashes.lower_bound(newest+1));
 }
 
-void CNetServerTurnManager::InitialiseClient(int client, u32 turn)
+void CNetServerTurnManager::InitialiseClient(int client, u32 turn, bool observer)
 {
 	NETSERVERTURN_LOG("InitialiseClient(client=%d, turn=%d)\n", client, turn);
 
 	ENSURE(m_ClientsReady.find(client) == m_ClientsReady.end());
 	m_ClientsReady[client] = turn + COMMAND_DELAY_MP - 1;
 	m_ClientsSimulated[client] = turn;
+	m_ClientsObserver[client] = observer;
 }
 
 void CNetServerTurnManager::UninitialiseClient(int client)
@@ -187,6 +197,7 @@ void CNetServerTurnManager::UninitialiseClient(int client)
 	ENSURE(m_ClientsReady.find(client) != m_ClientsReady.end());
 	m_ClientsReady.erase(client);
 	m_ClientsSimulated.erase(client);
+	m_ClientsObserver.erase(client);
 
 	// Check whether we're ready for the next turn now that we're not
 	// waiting for this client any more
diff --git a/source/network/NetServerTurnManager.h b/source/network/NetServerTurnManager.h
index 2eb3b81b50..1ac71ec7eb 100644
--- a/source/network/NetServerTurnManager.h
+++ b/source/network/NetServerTurnManager.h
@@ -1,4 +1,4 @@
-/* Copyright (C) 2018 Wildfire Games.
+/* Copyright (C) 2021 Wildfire Games.
  * This file is part of 0 A.D.
  *
  * 0 A.D. is free software: you can redistribute it and/or modify
@@ -18,16 +18,18 @@
 #ifndef INCLUDED_NETSERVERTURNMANAGER
 #define INCLUDED_NETSERVERTURNMANAGER
 
-#include <map>
 #include "ps/CStr.h"
 
+#include <map>
+#include <unordered_map>
+
 class CNetServerWorker;
 class CNetServerSession;
 
 /**
  * The server-side counterpart to CNetClientTurnManager.
  * Records the turn state of each client, and sends turn advancement messages
- * when all clients are ready.
+ * when clients are ready.
  *
  * Thread-safety:
  * - This is constructed and used by CNetServerWorker in the network server thread.
@@ -43,13 +45,13 @@ public:
 	void NotifyFinishedClientUpdate(CNetServerSession& session, u32 turn, const CStr& hash);
 
 	/**
-	 * Inform the turn manager of a new client who will be sending commands.
+	 * Inform the turn manager of a new client
+	 * @param observer - whether this client is an observer.
 	 */
-	void InitialiseClient(int client, u32 turn);
+	void InitialiseClient(int client, u32 turn, bool observer);
 
 	/**
-	 * Inform the turn manager that a previously-initialised client has left the game
-	 * and will no longer be sending commands.
+	 * Inform the turn manager that a previously-initialised client has left the game.
 	 */
 	void UninitialiseClient(int client);
 
@@ -73,6 +75,9 @@ private:
 	/// The latest turn for which we have received all commands from all clients
 	u32 m_ReadyTurn;
 
+	// Client ID -> whether they are only an observer.
+	std::unordered_map<int, bool> m_ClientsObserver;
+
 	// Client ID -> ready turn number (the latest turn for which all commands have been received from that client)
 	std::map<int, u32> m_ClientsReady;
 
@@ -84,7 +89,7 @@ private:
 	std::map<u32, std::map<int, std::string>> m_ClientStateHashes;
 
 	// Map of client ID -> playername
-	std::map<u32, CStrW> m_ClientPlayernames;
+	std::map<int, CStrW> m_ClientPlayernames;
 
 	// Current turn length
 	u32 m_TurnLength;
diff --git a/source/ps/scripting/JSInterface_Game.cpp b/source/ps/scripting/JSInterface_Game.cpp
index fdce7dbe22..7b06c84783 100644
--- a/source/ps/scripting/JSInterface_Game.cpp
+++ b/source/ps/scripting/JSInterface_Game.cpp
@@ -98,6 +98,17 @@ void SetSimRate(float rate)
 	g_Game->SetSimRate(rate);
 }
 
+int GetPendingTurns(const ScriptRequest& rq)
+{
+	if (!g_Game || !g_Game->GetTurnManager())
+	{
+		ScriptException::Raise(rq, "Game is not started");
+		return 0;
+	}
+
+	return g_Game->GetTurnManager()->GetPendingTurns();
+}
+
 bool IsPaused(const ScriptRequest& rq)
 {
 	if (!g_Game)
@@ -179,6 +190,7 @@ void RegisterScriptFunctions(const ScriptRequest& rq)
 	ScriptFunction::Register<&SetViewedPlayer>(rq, "SetViewedPlayer");
 	ScriptFunction::Register<&GetSimRate>(rq, "GetSimRate");
 	ScriptFunction::Register<&SetSimRate>(rq, "SetSimRate");
+	ScriptFunction::Register<&GetPendingTurns>(rq, "GetPendingTurns");
 	ScriptFunction::Register<&IsPaused>(rq, "IsPaused");
 	ScriptFunction::Register<&SetPaused>(rq, "SetPaused");
 	ScriptFunction::Register<&IsVisualReplay>(rq, "IsVisualReplay");
diff --git a/source/simulation2/system/TurnManager.cpp b/source/simulation2/system/TurnManager.cpp
index 0dd07b65ef..100a960cd6 100644
--- a/source/simulation2/system/TurnManager.cpp
+++ b/source/simulation2/system/TurnManager.cpp
@@ -1,4 +1,4 @@
-/* Copyright (C) 2020 Wildfire Games.
+/* Copyright (C) 2021 Wildfire Games.
  * This file is part of 0 A.D.
  *
  * 0 A.D. is free software: you can redistribute it and/or modify
@@ -36,20 +36,6 @@
 #define NETTURN_LOG(...)
 #endif
 
-/**
- * Maximum number of turns between two clients.
- * When we are on turn n, we schedule new commands for n+COMMAND_DELAY.
- * We know that all other clients have finished scheduling commands for n,
- * else we couldn't have got here, which means they're at least on turn n-COMMAND_DELAY+1.
- * We know we have not yet finished scheduling commands for n+COMMAND_DELAY, so no client can be there.
- * Hence other clients can be on turns [n-COMMAND_DELAY+1, ..., n+COMMAND_DELAY-1], and no other,
- * hence any two clients can only be this many turns apart.
- */
-constexpr int MaxClientTurnDelta(int commandDelay)
-{
-		return 2 * (commandDelay - 1);
-}
-
 const CStr CTurnManager::EventNameSavegameLoaded = "SavegameLoaded";
 
 CTurnManager::CTurnManager(CSimulation2& simulation, u32 defaultTurnLength, u32 commandDelay, int clientId, IReplayLogger& replay)
@@ -58,8 +44,7 @@ CTurnManager::CTurnManager(CSimulation2& simulation, u32 defaultTurnLength, u32
 	m_FinalTurn(std::numeric_limits<u32>::max()), m_TimeWarpNumTurns(0),
 	m_QuickSaveMetadata(m_Simulation2.GetScriptInterface().GetGeneralJSContext())
 {
-	// Lag between any two clients is bounded. Add 1 for inclusive bounds.
-	m_QueuedCommands.resize(MaxClientTurnDelta(m_CommandDelay) + 1);
+	m_QueuedCommands.resize(1);
 }
 
 void CTurnManager::ResetState(u32 newCurrentTurn, u32 newReadyTurn)
@@ -237,16 +222,23 @@ void CTurnManager::AddCommand(int client, int player, JS::HandleValue data, u32
 {
 	NETTURN_LOG("AddCommand(client=%d player=%d turn=%d current=%d, ready=%d)\n", client, player, turn, m_CurrentTurn, m_ReadyTurn);
 
-	// Reject commands for turns that we should not be able to compute (in the past or too far future).
-	if (m_CurrentTurn >= turn || turn > m_CurrentTurn + MaxClientTurnDelta(m_CommandDelay) + 1)
+	// Reject commands for turns that we should not be able to compute (in the past).
+	if (m_CurrentTurn >= turn)
 	{
-		debug_warn(L"Received command for invalid turn");
+		// The most likely explanation is that an observer that's lagging behind is sending commands,
+		// which is possible when cheats are enabled. Report & ignore.
+		// It seems a bad idea to error out too badly here:
+		// nefarious clients could try and send broken commands to DOS.
+		LOGWARNING("Received command for invalid turn %i (current turn is %i)", turn, m_CurrentTurn);
 		return;
 	}
 
 	m_Simulation2.GetScriptInterface().FreezeObject(data, true);
 
 	ScriptRequest rq(m_Simulation2.GetScriptInterface());
+	size_t command_in_turns = turn - (m_CurrentTurn+1);
+	if (m_QueuedCommands.size() <= command_in_turns)
+		m_QueuedCommands.resize(command_in_turns+1);
 	m_QueuedCommands[turn - (m_CurrentTurn+1)][client].emplace_back(player, rq.cx, data);
 }
 
diff --git a/source/simulation2/system/TurnManager.h b/source/simulation2/system/TurnManager.h
index f557f134c8..588d57e8cb 100644
--- a/source/simulation2/system/TurnManager.h
+++ b/source/simulation2/system/TurnManager.h
@@ -1,4 +1,4 @@
-/* Copyright (C) 2020 Wildfire Games.
+/* Copyright (C) 2021 Wildfire Games.
  * This file is part of 0 A.D.
  *
  * 0 A.D. is free software: you can redistribute it and/or modify
@@ -155,7 +155,13 @@ public:
 	void QuickSave(JS::HandleValue GUIMetadata);
 	void QuickLoad();
 
-	u32 GetCurrentTurn() { return m_CurrentTurn; }
+	u32 GetCurrentTurn() const { return m_CurrentTurn; }
+
+	/**
+	 * @return how many turns are ready to be computed.
+	 * (used to detect players/observers that fall behind the live game.
+	 */
+	u32 GetPendingTurns() const { return m_ReadyTurn - m_CurrentTurn; }
 
 protected:
 	/**