Quests are given by different NPC's in the game. They offer rewards for completion like money, items and diplomatic points. Quests appear randomly throughout both the Old World and New World, but can also be requested from other A.I players. Quests are also differentiated by type: the type of quest is displayed to you before you accept the quest but the objectives will only be displayed upon accepting the quests. The player is given a 30 minute timeframe to complete the vast majority of quests.
Some quests form a 'chain', and completing the first quest will provide access to another quest with a continuing narrative. Progressing through chain quests often has better rewards than completing standalone quests, and chain quests can be identified by having a number at the end of the name of the quest.
Different computer characters have different possible quest rewards with the rewarded items being themed to their backstory, such as Bente Jorgensen often giving animals as rewards.
Types of quests
Different quest givers are more or less likely to give you certain quest types. For example, Neutral Traders will never give you puzzle quests, while Bente Jorgensen will never give you destruction quests.
Puzzle quests require the player to solve a puzzle of some sort, relating to their islands. Most puzzle quests will require the player to locate clickable entities, in a sort of "Where's Wally" game. This has been made easier from prior Anno games; not only are hints provided as to the location, but clicking the quest description will snap the player to the area the entities are in.
Often given by citizens from the Engineer tier, these quests are given in the form of a riddle for which the answer is one of the buildings the player has on their islands. The quest can be completed by clicking on the appropriate building (which may be in a different region to the quest-giver). The quest log contains the enigma message. These riddles will always point to a building that the player has already built; if one is not present, the quest will not fire.
Destruction quests ask the player to use their navy to chase down and sink a ship or group of ships. These can vary dramatically in what sort of ships they are and how many of them there are. Some Destruction quests will also be on a much more stringent timer as the ships will attempt to leave the region.
Photography quests ask the player to use the postcard-view camera to photograph a certain building or event. The camera will produce crosshair markers around the edge of the frame when pointed at the correct place.
Pick up quests
Usually the simplest quests, pick-up quests ask ask the player to pick up a good or package at one location and move it to another. This can be an item from a ship at sea or in harbor, or it can be flotsam at a location in the ocean. Many of these are relatively short-ranged. Some of them are not, and will require moving goods from the New World to the Old World or vice-versa. Others may require multiple stages of delivery, picking up a number of objects at the start and taking one each to widely dispersed targets.
Similar to Pick up quests, these quests ask you to sail to a certain location and pick up an item, but the location will be guarded by a number of AI-controlled ships which sail in a circle around the objctive. You will need to avoid sailing near the ships (their vision radius is displayed as a green circle which turns red upon sailing into range). If you stay within the vision range of one of the defending ships for too long the quest will fail.
Delivery quests ask the player to deliver a quantity of resources to a target ship. Just about any sort of resource can be asked for, though construction materials such as timber and bricks are relatively common. While straightforward, these quests can ask for resources that are difficult to provide or must be denied to citizens to gain enough of in the time limit.
The player's citizens may also ask them to undertake these quests, in which case the resources need to be put into the Warehouse storage for the island the citizen is on.
Escort quests have the player use their navy to escort NPC ships from one place to another, and sometimes out of the region. Along the way, these ships will usually be attacked by one or more waves of enemies who must be killed. Naval ships can be ordered to escort another ship by right-clicking directly on the ship, after which they will do their best to keep pace with the ship and engage any enemies who try to attack it.
Similar to Escort quests, Follow quests quests ask you to use one of your ships to follow an NPC ship, but in this case the quest will fail if you either get too close to the ship or get too far away from it for a period of time. These quests often require active micro-management of your ships to stay within the correct range of the target.
Construction quests usually appear (if at all) shortly after the player has advanced to a new level of citizenry. The quest-giver will ask the player to build a building from the new unlocked set--Willie Wibblesock, for instance, can ask them to build a Variety Theater. The player's citizens can also make these requests--Obradors can ask for a Town Hall, for example.
Computer opponents will (rarely) offer you quests to sustain a certain item of your economy for a period of time. The quest objective could be to keep your income above a certain level, keep your happiness high for a period of time, keep your population satisfied with a certain good for a period of time, or to keep a certain amount of a good in your warehouse for the duration of the quest.