Zombies are usually unintelligent undead, essentially reanimated corpses that seek to terrorize and consume the living. They can also be living humans infected with a terminal, rabies-like disease.
More recently, movies have featured faster running zombies and zombies that are not dead, but instead the victims of bio-weapons or a plague. These living zombies are usually not any different from the undead variety, except that they can usually run faster and be killed easier.
