Jet and Faye are after Starship Pirates, while Spike is bringing his ship to be overhauled. After Spike's return to the Bebop, he finds out that Jet and Faye didn't capture the bounty heads. The Starship Pirates have a virus that they transmit by harpooning ships. As long as they avoid getting harpooned, they'll be OK. If they do get harpooned, Jet's solution is to turn of their ships' computer systems and fly them manually. One misstep on Spike's part, and he's a dead man.
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.