The aliens are invading Earth, and it's up to the "Alien Busters" to wipe them out and destroy their creator. The Busters consist of Karla, Gordon, and Scooter. Each one of them have their own weapons and special attacks.
When you start the game, you can select any one of these characters to play as. There are six missions to complete (eight in the Genesis version) with several stages, and each mission has you blasting aliens all the way to the end, from the streets to the mother ship where you'll meet the mother of all aliens. Unfortunately, blasting these aliens will not be an easy task, as they get tougher in every mission, and are capable of hiding into objects such as plants, postboxes, trashcans, drums, and several others. Each mission has an objective such as rescuing people destroying an UFO.
You can play Alien Storm by yourself, or with another person.