It is not the best description, but Cowboy Bebop is an anime that is most accurately described as a tragic space opera whose characters are embedded in Western’s and Film Noir. That is a mouthful though, let’s start from the beginning.
A hyper-gate has exploded in outer space, damaging the moon, and sending debris down to an unsuspecting Earth. Ravaged by the falling rocks, millions die, and large areas are ruined by the numerous impacts. The incident has caused Earth’s remaining population to leave and settle elsewhere, colonizing the moons of Jupiter, Mars, and several large. To police an entire galaxy and protect it from the rule of the new crime syndicates, an old west style bounty hunter system has been put into place, and these hunters are referred to as Cowboys.