A few Causes of War, such as the Crusade or Jihad, are linked to Art of Diplomacy's new religion dynamic. Religion makes its triumphant return to the Civ franchise, with six new religions: Buddhism, Hinduism, Taoism, Islam, Christianity and Judaism. Art of Diplomacy adds new Religious city-states, like Vatican City or Jerusalem, who will strongly favor civilizations that share their state religion and gift them espionage points and units. Other civilizations who share your civilizations will not like or dislike you any more, however, both they and city-states will join you on Ecclesiastical Councils of the Faith.
These Faith Councils vote collectively to assign cities, create defensive pacts, excommunicate other factions, adopt a group certain social policies, divide newly discovered lands, etc. put forth but the Council Head. Councils can vote to launch Crusades against nearby civs of a different religion (civs that have adopted NO state religion cannot be a target), giving all council members a Cause of War against the target civ that ends if the Civilization adopts YOUR state religion. Civs can also vote on a Jihad, where all civs sharing that faith declare war if a civilization with a different State Religion declares war on one of its members. Especially watch those city-states here, if Christian Vatican City despises Islamic Jerusalem it may convince it's fellow Christians to Crusade against the little upstart. However, the Islamic council may vote to Jihad in response, and what started as a dispute between two city states now involves war between 5 civs and 9 city-states.
Religions are founded by researching appropriate techs, selecting the right social policies and then spending culture points. Founding a religion will let you put that Religion's Holy Place in one of your cities, where it will generate culture and increase your empire's happiness as long as you adopt the appropriate State Religion. But most important, the owner of the Holy Place will break any tie in the event of a deadlock vote in the Faith Council.
Those votes are important for another reason, because once a vote on an issue has been declared you can attempt to buy or sell votes. Buying a civs votes can be expensive, but may prove worthwhile. You can either barter a future council vote, but be wary, once you've sold it you can't get it back. If the next vote should be something that disfavors you (like assigning one of your cities to a brother in the faith) you'll have to grit your teeth and hope for the best because you'll have no say while your other "brother" will.
If a vote goes against you can defy the will of the council. However, you may wind up excommunicated for your troubles, which grants the crusade Cause of War to all of your former brothers and greatly upsets your citizens.