Requirements for being chosen as a Caliph?

Spawned from this question what is the requirements for becoming and remaining a Caliph (or ruler in general) according to Islam? Is there any requirement at all or whoever could reach the power and get the pledge of allegiance (even through force and intimidation) is righteous to be treated as a Caliph, rebelling against whom being forbidden? *I believe the requirements should be general such that they hold about the 4 first Caliphs as well.*