There are 6 difficulty levels in Vanilla and Play the World, and 8 in Conquests. They are: Chieftain, Warlord, Regent, Monarch, Emperor, (Demigod), Deity, (Sid). The parenthesized ones are Conquests-only. At Warlord and Chieftain, you'll have a weaker AI that is penalized (it takes them longer than you to build things, research techs, etc.). At Regent, the AI and you don't have any advantages nor disadvantages. Above Regent, the AI starts to get some bonuses, like extra units at the beginning of the game, faster production and research, lower corruption, etc.