It begins with Faye complaining about the Bebop's shower. Her nagging of Jet leads to a question about his arm. Then an old partner of Jet's during his days with the ISSP, Fad, calls up wanting to team up with Jet one last time. Fad wants to go after a runaway prison ship that happens to be carrying an old enemy of Jet's, Udai Taxim, who used to be an assassin for the syndicate. Udai had something to do with Jet losing his arm. Jet at first refuses, but finally decides that this is something he must do.
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.