Spike and Jet are after a man named Abdul Hakim who is on the run after stealing a very valuable briefcase from a laboratory, though what makes it difficult is because Hakim usually gets plastic surgery to avoid being spotted. While Spike goes out to look for Hakim, a two-bit thief manages to steal Hakim's briefcase and manages to slip away before Hakim grabs him. The thief eventually opens the briefcase and discovers that it's just a common Welsh Corgi that isn't worth more than a fistful of Woolongs, so why is Hakim after the dog so badly?
In the year 2071 humanity has colonized the entire Solar System through the use of 'Phase Difference Space Gates'.
A catastrophic accident occurred during the development of the Gates, damaging both the Earth and the Moon, heavily irradiating the surface, and forcing most of mankind to evacuate to other planets of the Solar System.
Wherever humanity goes, so goes its criminal element, and thus the need for those who hunt criminals. The newly formed solar system police reinstated the bounty scheme of the Wild West. Cowboy Bebop is the story of the four inhabitants of the spaceship Bebop, and the living they barely make at bounty hunting.