What follows is an overview of the main story of Cowboy Bebop that does not contain spoilers.
In 2022, an experimental hyperspace gateway designed to make high-speed outer space travel possible malfunctioned and exploded, destroying much of the Moon. Consequently, the Earth became continuously bombarded with radiation and debris, posing a grave threat to the inhabitants of the planet. With no options left, humans turned to outer space travel, terraforming the other planets of the Solar System. In time, they perfected the technology of the astral gates and developed thriving civilizations on many of these planets, most notably Mars, the new hub of human civilization.
Politics, society, and economics changed with the times. New generations grew up with no memories of the Earth, and ethnic groups and nations gave way to planetary allegiances. As these new communities flourished, the economy boomed (similar to the economic productivity nations encountered after World War II). However, this also widened the disparity between the rich and poor, and interplanetary crime syndicates began to exert influence over the planetary governments and the Inter-Solar System Police (ISSP). In order to control the criminal activity, a "bounty-reward scheme" was introduced.
Cowboy Bebop takes place in the year 2071. The crew of the spaceship Bebop is a partnership of bounty hunters, called "cowboys," who travel the Solar System trying to apprehend various criminals and lawbreakers. Jet Black is the owner of the Bebop and partners up with Spike Spiegel, a young man with versatile combat skills. Though he is reluctant to admit it, Jet has also come to rely on Spike for companionship in the normally solitary field of bounty hunting. Soon enough, they are joined by Ein, Faye, and Edward, making for a diverse (but perpetually poor) group.
Most of the episodes are self-contained and revolve around attempts to bring in a specific bounty. Some of the bounty hunters' various targets include small time thugs, gangsters, hackers (known as "Net Divers" in slang), cult leaders, psychopaths, genetic experiments, mutant creatures and petty thieves. However, the show often shares its focus with the histories of each of the main characters and of more general past events in the Bebop universe, which are gradually revealed as the series progresses.
Main article: Session List
Each episode of the anime is known as a "session." The main story takes place over 26 sessions and a movie, although other Cowboy Bebop media also exists.