The Pope is the head of the Catholic Church, and is the head of the Papal States Faction. The Pope can excommunicate a faction. Excommunication causes religious unrest within the affected faction and also means a Crusade can be called against a Catholic faction.
College of Cardinals
The College of Cardinals is an organization of catholic priests that is centered in Rome. It is formed of the most pious priests in Christendom, and any sufficiently religious priest can be selected for it, if one of the thirteen seats is open. Contrawise, if there are no priests of high enough Piety(5) then no more seats in the College of Cardinals will be filled until this criterion is met. Cardinals usually remain under their faction's control, simply gaining an extra piety point from the "Cardinal" trait. However, whenever the Pope dies, an election is held among the College to determine the next pope.
To start a crusade you must go to the pope overview scroll, which is a tab within the faction information menu (Press your faction shield in the campaign map UI, at the bottom right(ish) of the screen). From the pope overview scroll request the pope to call a crusade via the "request crusade" button, depending on the pope's relationship level with your faction, you may or may not have to pay an amount of money. Once the crusade has been called you must then join the crusade, or suffer lower relations with the Pope (see below).
Once the Pope has called for a crusade, regardless of origin, the player may join it provided unless currently excommunicated. To join the crusade you must have an army with more than 8 units in it. Once you do, select that army, and press the "Join Crusade" button. You can have more than one crusading army at a time. All armies selected to join the crusade will now become a crusading army, which has free upkeep for all units and double movement points (even when being transported by ships). Furthermore, joining a crusade opens access to recruit crusader mercenaries, such as crusader sergeants, turkupoles, and grand crosses which inspire your men and swell its ranks. However, units can only leave the crusading army if it captures a settlement, and if the army doesn't move fast enough, men will begin to desert, disappearing from the army stack.
Crusades give bonuses in terms of experience for all units involved, as well as chivalrous traits for any generals who lead crusading armies, even if their army doesn't take the crusade objective (except if they abandon the crusade of course). Furthermore, joining crusades allows guilds of crusading orders of knights to be built.
In order to request a Jihad, the player must click on an Imam and look for the Call Jihad button. The Imam has to have a piety of at least 4 to request a Jihad. However, they cannot be called in quick succession. Jihads have the same problems and benefits of a crusade.
The Aztec Empire is the only genuinely Pagan faction in the vanilla version. However, several rebel regions - such as Stettin - start out pagan and must be converted.
The rebel faction is the only faction which supports Heretic characters.
Religious Agents appear on the campaign map and have a primarily religious affect.
Priests and Imams
Priests and Imams are essentially the same type of agent, Priests being the Christian version, and Imams the Islamic version. They are recruited from settlements that have their corresponding religious buildings, and when left in a region, they will convert the people of that region to their religion, based on the rate of how much religious skill they possess.
Heretics are campaign map characters that increase the level of Heresy in the regions they pass through. They are effectively Priests for the Rebels faction.
They may be denounced (in other words, burned at the stake) by a Priest or Imam. The chance of success depends on the Priests piety and that of the Heretic; if they are equal there is a 33% chance of success. If the priest or imam fails he may transform into an heretic himself, as the Heretic convinces him that he is right. Cardinals and Religious Agents with 6 or more Piety are immune to Heresy.
Witches are similar to Heretics in that they spread Heresy. The only notable difference is that they are female, and the fact that they can curse any general they come in contact with (shows up in the general's character traits).
They may be denounced (killed) by a Priest or Imam with a high enough religious skill. They may kill priests and imams attempting to denounce them.
- For more details on this topic, see Inquisitors.
"An Inquisitor is a special sort of priest, sent by the Catholic church to 'deal with Heresy' when it becomes a serious problem in the Pope's eyes."
- -The Creative Assembly, Official Medieval II: Total War manual
Inquisitors are special agents sent by the pope to deal with provinces that have especially high heresy levels. These agents have the power to "denounce" any characters they suspect of blasphemous behavior, whether they be priests or even Faction Leaders, though they usually deal with Witches and Heretics before moving to denounce your generals.
Denouncing a character has the effect of putting him up to trial for heresy. If found guilty, the accused character will be executed. Inquistors' piety level directly affects their chances of successfully convicting your characters of heresy, while on the other hand, your generals' piety levels directly affects their chances of surviving.
Inquisitors, like any other campaign map character, can be assassinated. However, since they represent the Papal States, there may be some serious diplomatic consequences for attempting and failing this.