The Greek gods, led by Zeus, overthrew the Titans and established their rule on Mount Olympus. After a prophecy foretold his downfall by a marked warrior, Zeus sent Ares and Athena to find him, leading to the gods' interference in the lives of Kratos and his brother, Deimos. This resulted in Kratos's descent into a life of vengeance, where he killed his family at Ares's command, became the new God of War, and eventually waged a war against the entire Olympian pantheon to kill Zeus.
There are other regions besides Greece where other types of gods reside. Though these gods have not done any harm to Kratos himself, he still finds it hard to trust any god and believe that they are all the same, no matter where they come from.
Will Kratos find the vengance he wants for the family he lost? Or will he succumb to the power of the gods. Will Kratos find himself a peaceful life? Or will he continue to hunt gods until every last one is dealt with? That is up to the player.