In Anno 1800, in the case that a war breaks out between 2 players or a player and one of the pirate leaders, it is fought entirely by their Navies. To conquer an island by military means, a player has to emerge victorious in a Siege on the island's defenses.
Starting a war[]
Direct declaration of war[]
In order to engage in combat with any enemy faction, the player has to first declare war on said faction via the Diplomacy menu (middle button below the minimap). Alternatively, another faction may declare war on them. In either case, the start of a war with an AI will cause the player's Diplomatic Reputation with that AI to immediately drop to 0. The player will start the game at war with no other faction except for Anne Harlow. Most player AI's will declare war when the reputation with the player is bad, and are more inclined to do so if the player's military is particularly weaker than theirs. Both Anne Harlow and Jean La Fortune will demand tribute (threatening war) from time to time, even when the player has great reputation with them. Specifically Jean La Fortune will, despite starting at peace with the player, soon demand a high sum of money to keep that peace - and continue to do so every so often despite the improvement of one's own reputation with him, meaning a chain of ceasefires will ultimately be much cheaper for the player.
To avoid being declared war on, maintaining good relations with the AI early on is adviced. Expert AIs are more likely to declare war on a player than Normal ones, and Easy AI will not go out of their way to declare war when possible.
While having a Non-Aggression-Treaty running with a faction, the player cannot declare war on them directly, nor will they be able to declare war on the player directly.
Alliances[]
Allying with a player AI will FORCE the player to join any new wars they start or when another AI declares war on them, disregarding your reputation, ceasefires or Non-Agression-Treaties with them. Therefore it is ill-adviced to ally with certain AI's: While Easy AI's are not the kind that would declare war on anyone and it's very easy to gain reputation/ally with them, they eventually will be natural prey for any other harder AI and pull you into that war when allied to them.
Having a good standing with either of the two Pirates is a great source for 
Gold Bars and Special Ships Allying with a player AI, who's almost certainly at war with Pirates, will cause the player's reputation with the respective Pirate faction to drop to 0 each time a ceasefire of the AI ends (The exception to this is Lady Margaret Hunt, who is always peaceful with Anne Harlow).
If the player is allied to two factions that declare war on each other (one of which may be a Pirate in this case), they're left with the choice of siding with either side, or terminating their alliances with both (leaving them at trading treaties and ~80 reputation).
In Multiplayer[]
Wars and other treaties with human players in Multiplayer are started and ended with a press of a button in the Dimplomacy menu, as reputation is not a statistic with them.
Once in a war, the player has 2 options: Putting a stop to the war or fighting it out in combat.
Ending a war[]
Peace is good for business. A player that doesn't want to be a conqueror or even build warships to defend their territory can always find ways to stop the fighting, provided they have some money to spare.
Ceasefires[]
Ceasefires can always* be arranged with an enemy faction, as long as the faction is not annoyed by that conversation topic because of previous failed attempts at negotiating one (e.g. declining an offer). In that case one has to wait until the chance of succes is not zero anymore. Negotiating a ceasefire will usually cost a small sum of money (the more reputation the less it costs), and, most importantly, when a ceasefire is accepted the player will gain 5* reputation with that enemy. Chaining ceasefires is both the easiest way of avoiding combat with the AI as well as the basis of negociating Peace with them again.
The Peace Treaty[]
When a player has enough reputation that a Peace Treaty is no longer 'impossible' in the Diplomacy menu (≥30 reputation, sometimes more)*, proposing one will usually be met with some cost to it, but ultimately end the war and once again have the player gain a decent chunk of reputation with the AI.
*Needs confirmation
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Main article: Naval Combat
Any military 
ships the player builds in their shipyards have significant strengths and weaknesses based on their type. Therefore, planning and preparation is adviced; not only should one think about what types of ships they'll need in the future to best fit their plans, but producing them far before a war has even broken out is crucial - building a 
Battle Cruiser will take as much as 15 minutes.
If you have a Navy at the start of the war, it is important to make most of it. This is both by having your navy in the right places at the right times, while continuing to build the ship types that fit your situation best (commonly refered to in RTS games as 'macro'), as well as understanding one's ships' individual best usage and being able to command each ship in your fleet indivadually during a battle to maximize their effectiveness (known as 'micro'). As the outcome of wars is primarely decided at sea, in big clashes of the opposing navies but also with tactics to harass or disrupt enemy trade routes, being experienced with Combat in Anno 1800 will increase your chance of winning your wars significantly!
Island Sieges[]
When the first shot is fired against a settled island, it is considered under siege. This event is announced to every player in the game, even those not involved in the war. If the island's defenses stop recieving damage in a while, a warning is given to the attacker that the siege will end shortly, and if he doesn't re-engage in the attack for a couple of minutes the siege ends officially.
The defending player can continue to build structures including turrets in the harbor during the siege, provided he has the resources to do so. However, like the buildings that handle catastropies (e.g. Fire Stations), any newly built turrets take a while to come online and commence firing, but can already be attacked during this time.
To win a siege, the defending island's 'morale' has to be dropped significantly until they surrender. The islanders' morale is directly related to the combined health points of all harbor defenses and other harbor buildings and starts at 100%. While the harbor is being destroyed, the moral decreases accordingly, eventually resulting in a massive loss of the population's happiness and therefore riots.
Once the morale drops below 30%, the island goes 'critical'. If the morale doesn't recover and the island remains critical for a while, it is certain to surrender eventually. The time the island waits until surrender can further be reduced by continuing effort to decrease the morale, up to the point where the island surrenders immediately at 0% morale.
Once the island has surrendered their defenses stop firing and the victor is met with a special screen that gives them 2 options: To take over the island or to claim 100% of their shares. If the attackers consisted of more than 1 player, they may only claim shares and the shares will be split between them.
Taking over the island[]
If the victor decides to choose this option, every building and road on the island is removed apart from the harbor warehouse, which too is left completely empty but keeps the level it was upgraded to. The addition of the new island to one's empire does cost Influence, but it is still an option to conquer the island and have negative influence points if one is lacking the required points for an island.
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By claiming the shares of the island, the defeated player is left in charge but loses all of the 5 island shares to the enemy. This leaves the victor(s) with a constant stream of money while the loser only gains a small fraction of the island's income.
After a player's island is defeated in a siege, it cannot be sieged again for 30 minutes by any player. You can find the remaining cooldown under the city name at the top of the screen.
Both pirates' nests are defeated similarly to players' islands. However there is no option to take over the island or claim any shares; Instead, eradicating the nest will remove the faction from the respective session for a while.
Main article: Pirates
Fitting war efforts with economy[]
-to be added- (on costs and influence costs of a standing navy, production costs and benefits and how to not be the winner of the arms race of naval power and getting away with it)
Historical context[]
-to be added-