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Like most 4X strategy games, Age Of Wonders 4 offers multiple victory conditions by which players can get themselves a win. They're not as straightforward as you might think, and most can even be interrupted, so it's far less likely that a player who's established a dominant position early will simply run away with the entire campaign.
This guide will take you through all the standard victory conditions and how to achieve them. It's worth keeping your options open for the first half of the game, then pick a goal and push for it when things start to get tense.
Military Victory
The most basic victory condition is the Military Victory, which you earn by eliminating every other major empire. Free Cities and Vassals don't need to be taken out, just the Rulers shown in the top-right corner of the screen.
Rulers with whom you have an Alliance, either through diplomacy or by subjugating them through a war, don't count toward the number of empires you need to defeat. If the only Rulers left on the map are your Allies, you'll claim a Military Victory.
A Ruler is eliminated from the game if they are banished to the Astral Void - that is, reduced to zero Health in battle - while they do not control their Throne City. If both of those conditions are met, the Ruler is immediately and permanently taken out of the game. You can achieve these goals in any order, either taking out the Ruler and then conquering their Throne City before they respawn, or taking the city first then hunting down and eliminating the Ruler.
Early on, you may not need to wage a full-scale war to defeat a weaker Ruler. If another player is besieging their Throne City, and you have an opportunity to kill the Ruller, you can eliminate them from the game without committing to an invasion yourself! The player that eliminates another Ruler will usually get an event that offers them a choice of bonuses.
Expansion Victory
If you control the overwhelming majority of territory on the map, you can claim an Expansion Victory. The first step is to control as many Provinces as possible - the exact number varies by map, and can be seen in the Quests tab.
Due to the city cap and the speed at which cities annex new Provinces, it's unlikely that you'll ever control the amount of necessary land directly. However, Vassal cities whose Allegiance level is Bonded or higher count their territory toward your total. Therefore, the best way to achieve an Expansion Victory is to vassalize as many cities as possible, either through diplomacy or force. Note that in the latter case, though, it will take longer to get your subjects to the necessary level of loyalty!
Once you control the requisite number of Provinces, you'll be able to build the Beacons Of Unity. These special Province Improvements must each be built in separate cities, but you can have more than one under construction at a time. You can't have more than three Beacons of Unity; if the third one is finished while others are under construction in your empire, the extras are canceled.
Once you've started construction on the Beacons, you don't need to keep your territory over the limit. You'll obviously want to do so for all the benefits of controlling so many Provinces, but you can afford to lose a vassal if things get dire.
When all three Beacons of Unity are built, click on any one of them and choose to Light The Beacons. Doing so starts a fifteen-turn timer, at the end of which you'll win the game. Don't get comfortable, though, you're going to have to fight for your victory!
Any turn that ends with an enemy stack on one or more Beacons doesn't count toward the timer. Expect the other players to declare war on you and attempt to take the Beacons. Worse, every few turns a large army of Marauders will spawn within your borders near a Beacon and attempt to occupy it! The Marauders won't try to destroy the Beacons, but as long as they occupy them you won't be able to win the game.
Rulers, on the other hand, will very likely try to pillage your Beacons. If they succeed in doing so, you'll need to rebuild them from scratch and start the timer over. The same goes for opponents who light their own Beacons Of Unity - destroy even one Beacon, and you'll set them back dozens of turns!
Spell Victory
This victory type is recommended for players who are heavily focused on a single Affinity. As you research advanced Tomes, you'll be able to create Special Province Improvements similar to the Beacons of Unity. Unlocking a Tier Three Tome allows you to build a Seed of that Tome's Affinity; Tier Four unlocks the Root, and Tier Five unlocks the Heart.
Like the Beacons, the Seed, Root, and Heart must each be built in different cities. Once you have all three buildings for a single Affinity, you'll be able to cast that Affinity's victory spell. Doing so starts a timer identical to that of the Expansion Victory, and you'll need to protect the Seed, the Root, and the Heart just like the Beacons.
The Marauders that appear will have the opposite Affinity to the one with which you're trying to win. For example, if you're attempting to bring about the Age of Nature, undead hordes dedicated to Shadow will appear, while the Age of Chaos will face resistance from Order-Affinity zealots.
Score Victory
The game tracks each player's overall score based on multiple factors; the number and size of their cities, the levels of their Heroes, the number of researches they've completed, and so on. If no player has achieved another victory condition by the end of Turn 150, the player with the highest score wins by default.
Special Victory Conditions
Some maps, particularly Story Realms, have unique victory conditions that let you win the game in other ways. These will all be explained in the map itself, but they usually revolve around defeating an exceptionally powerful Ruler who starts with extra cities, higher-level heroes, or other major benefits.
Maps with Special Victory conditions can still be won through normal means, but aggressively pursuing these alternate wins can result in a fast win for skilled players.