How do video game cameras work?

[Adny]

If the player goes off the map (like lets say in Amnesia there was an area where the player could get off the map accidentally) would camera be able to follow or it would the camera just glitch (because it cant find you)?

In Amnesia's case, there is no "player", just an invisible cylinder with 1 hand that can hold a lantern. There is no possibility of the camera "detaching" from the player. You could use a few script functions to distort the angle and field of view, but it is still technically part of the player.