It's a normal day on the Bebop for bounty hunters Spike and Jet, until they find out about a new bounty hunter. Asimov Solensan is going around selling a new drug that he stole from the syndicate. It is an eyespray called 'Bloody Eye' which makes all of its users very fast and almost invincible, but they also go crazy. Spike and Jet do whatever it takes to catch the culprit. At the same time the syndicate is trying to hug Asimov and get the drug back from him.
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?
Faye Valentine, a woman on the run from the authorities, is held captive by a casino owner who wants her to perform a simple task. If she does this, then all of her debt the authorities are so eager to obtain from her will be erased. At the same time, Jet has a premonition to take a chance with his hard earned money. The former cop and Spike head over to the same casino that Faye is now working at.
Faye has lost her money and is stranded in Jupiter's orbit with no fuel. She finds a destroyed ship floating nearby and inside finds a dying pilot who asks her to take a briefcase to the I.S.S.P. At the same time, Spike and Jet are getting ready to capture a bounty named Morgan, but when an eco-terrorist group called the Space Warriors hug Morgan first, they decide to go after a different bounty; the leader of the eco-terrorists!
Spike's past emerges to haunt him when a 28 Million Woolong bounty is placed on Mao Yenrai, the crimeboss of the Red Dragons. Faye goes after the bounty and is captured by a cold-hearted man named Vicious. Against Jet's will, Spike leaves to go after the murderer of Mao Yenrai and faces off against Vicious.
Jet and Spike are out chasing thier next bounty named Giraffe. When Spike is following Zebra, Giraffe's old comrade, he meets a kid named Wen, a musical child prodigy. There is something strange about Wen. Jet discovers that there is a connection between Wen and a stone Giraffe handed to Spike with his dying breath.
Jet, Spike, and Faye are after thier next bounty head, Decker. Spike gets a tip and is waiting for Decker in a bar along with every other bounty hunter in town. Faye is at an ice cream parlor waiting for Decker. Spike meets V.T., a female space trucker, by helping her beat up some of the crude bounty hunters in the bar during a fight. Faye sees Decker and gives chase, but with the high explosives he has he messes her ship up. The story of this episode revolves around the character of V.T.
When a commercial aircraft that is landing on the Venus colony gets hijacked, Spike and Faye are on board because they were anticipating that such would occur, in hopes of capturing the hijackers because they have bounties on their heads. However, when a passenger named Roco Bonnaro develops an interest in his Jeet Kune Do skills, Spike decides to give him some pointers. Roco gives Spike a package to hold onto, though Spike later discovers that Roco has a bounty on his head and he decides to go find him.
A satellite draws strange images on the surface of the planet Earth in South America. The police believe it was a prank by a hacker who hacked into the satellites mainframe. Jet and Faye go to Earth to try and find the hacker. Jet goes to find out what kind of hackers work the area. Jet finds out that 'Radical Edward' is responsible, but they soon find out that this is going to be different than they anticipated.
The Bebop is on its way to Ganymede, Jet's home when he was a cop, to deliver a bounty named Baker Panchorero. Jet starts to space out thinking about his old girl friend, Alisa, who left him years ago. The Bebop lands and while Spike and Faye cash in the bounty, Jet goes to 'Le Fin', the bar owned by Alisa. While Jet and Alisa are reminiscing about old times, Spike finds out that Alisa's current boy friend, Rhint, has a bounty on his head.
When Jet gets swindled by Faye, he loses all of his clothes, so he goes to the storage bay to get a blanket. While there, he gets bitten by an unknown creature, though he didn't get a good look at what it was. Spike and Faye dismiss it as a rat, though they soon discover that the scenario is much more serious than they realized, as one by one they fall victim by the creature until only Spike is left to deal with the problem.
Faye has stolen all the money and vanished. Ed is told to track her down on the computer. While Ed doesn't find Faye, she does find a mysterious code name, Julia, coming from the Blue Crow Bar on Jupiter's fourth moon, Callisto. Spike takes off for the moon, much to Jet's chagrin. With his partner gone, Jet begins to look for Faye.
Spike wakes up and discovers that he has only been shot with a tranquilizer. He slowly rises and continues his search for Julia. In Gren's apartment, Faye has been handcuffed by her host as he tells her the story of the one man he truly admired: Vicious.
Spike, Jet and Faye are each out catching a bounty. The bounty they were after, the mastermind behind a gate hack scam, wasn't among the bounties they caught. They have only one clue to help them find their man: four chess pieces, all kings.
Jet, Spike, and Faye are in need of money so Jet decides to catch a bounty head who is a con-artist. Meanwhile, needing to get it off her chest, Faye tells her life story to Ein to try to relieve her stress, though Spike winds up hearing her story, but will it change his opinion of her?
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.
The crew and the Bebop are stranded on a strange planet and they are out of food and fuel. Spike and Jet try to fix the Bebop and everybody is hungry. Spike tells Edward to go out and get some food. Ed takes Ein along and she rides off on her motor scooter in search of food.
A package arrives for Faye, and she leaves in a hurry when she finds out it was sent C.O.D. with no return address. Spike opens the package and finds a Beta video cassette. Jet and Spike go on a quest to discover what is on the tape.
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.
After playing pool one evening, Spike walks into the aftermath of a large battle between armed agents and a large man seemingly dressed for an evening at the opera. The large man attacks Spike with the largest possible arsenal that one person can carry. Defending himself as best he can, Spike barely makes it out of the battle alive. Awaking on the Bebop wrapped up in bandages, Spike rests as Jet goes to Bob, his ISSP source, for help.
After Jet receives a note from an old friend, he attempts to track him down but just finds a tombstone. While he's there, he finds a young girl who helps him dodge some mobsters. They soon realize that they can work together to help each other find Pao, but will it be in the manner that they expect?
While Spike is trying to find some food, he runs into a serial bomber; the Teddy Bomber who is trying to blow up a skyscraper. Will he be able to stop Teddy Bomber and collect the bounty on him?
This episode was temporarily removed from airplay on Cartoon Network after the September 11, 2001 attacks, but has since entered normal rotation.
While Spike is watching television he comes across a religious organization called Scratch, whoes leader had quite a huge bounty because he leads his followers to commit suicide, so the crew of Bebop go off to try to find Dr. Londes in order to collect the bounty on him.
Faye is studying the video from her youth that she found one day and she sees a waterfall. Ed sees it and states that she knows where that waterfall is so they set the Bebop's path to earth instead of Mars. Will Faye be able to find out about her youth and what about Jet and Spike who don't know that the ship is now heading for Earth?
Vicious heads to the Red Dragon Syndicate to put an end to Van, which are the leaders of the Syndicate. Meanwhile, Spike and Jet are at a pub in town when the Red Dragon Syndicate burst in and start shooting up the place. As the action intensifies, Jet and Spike once again find themselves in the middle of another mess, though certain events soon make them realize that this may be bigger than they expected.
Spike manages to convince Julia to leave with him and put their past behind them once and for all. However, Vicious has other plans and he doesn't intend on letting them just walk away. Spike and Julia now find themselves facing the greatest danger they've ever faced and the stakes are their future, their happiness and their lives.