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Games in which the player shoots things to progress, usually with a variety of guns, and other times with bows and arrows.

Science-fiction. Commonly including things like aliens, advanced technology, and settings of outer space or distant planets. 

Shoot 'Em Up or shmup games are a subset of shooter games where the player continually moves forward while waves of enemies enter the screen. Both shooting and dodging are critical to advancing. See also Bullet Hell.