A map-based campaign uses a map (well who'd have thought it!). This shows the extent of each player's empire and the territories that they control. The map can also be used to regulate movement and show the location of each player's army and characters.
The campaign rules that follow are an example of the first type of map-based campaign, where the map is used to simply show how large each player's empire is and what territories he controls. Refer to the rules to find out how this type of campaign works.
In the second type of map-based campaign, the location of each player's army is shown on the map. This is somewhat more easily said than done, as a campaign usually lasts for weeks, if not months, and the map will need to be permanently set up during this period. One solution is to mount the map on a cork board and use map pins to show the location of the armies, or use Blu-Tak to stick counters onto the map. There are campaign turns between battles, in which the players move their armies around the map. When armies move into each other on the map a battle is fought to determine the outcome of the encounter.
Map campaigns like this often include special rules to cover things such as scouts, supply, raising new troops, assassins, revolts and all kinds of other events. Often, this side of the campaign turns into a game in its own right and actually fighting battles on the tabletop becomes secondary to outmanoeuvring your opponent on the campaign map.
Sadly, while map-based campaigns like these offer the greatest number of possibilities in terms of what can be done, in the author's experience they very rarely work in practice unless they are played by a small group of very dedicated players. The reason is that in order for the campaign to work it is vital that any battles which result from movement on the map are fought out promptly, as otherwise the campaign will bog down waiting for the result of a certain battle.
The other problem is that a cunning General will do his best to make sure that when he fights a battle he has ensured that the odds are well in his favour and that he heavily outnumbers his opponent. This can result in very lop-sided games that are not all that much fun to play; what's more, once you've lost one battle things tend to 'steam-roller' and it becomes increasingly difficult to win future battles. For these reasons, it helps to keep map-based campaigns quite small and with limited objectives. It also helps to have a 'campaign umpire' who can force the players to fight their battles in time for the next campaign turn, and impose forfeits on players that do not. However, the best asset such a campaign can have is very dedicated players, who will play their battles before the next campaign turn and won't drop out when things start going against them.