The show is set in the year 100,000,000 AD, on a satellite which orbits Earth. This future Earth is never visited directly, though it is referred in dialogue as a peaceful utopia where there are no longer any problems to solve. All nations of the world have merged into one, and, according to Tuddrussel, there are "no wars, no pollution, and bacon is good for your heart."
Despite this cheerful vision of the future, the space station on which the characters live and from which they travel to the past is remarkably dystopic. It features a shooting range, a terrarium, and a prison for repeat offenders, but it is dank, outdated (for the time) and unclean. Mostly this seems to be down to Officer Buck Tuddrussel, a scruffy and immature perennial bachelor, who nevertheless happens to be the station's most senior officer. There were also several accidents aboard the Time Squad Space Station; most notable of which is the terrarium being broken after Tuddrussel plays golf and breaks the glass shell of the station. This action seems to have no consequences in future episodes.
The only other official member of Buck's unit is Larry 3000, a translator robot and former diplomat who was rendered more or less obsolete when all of the world's nations merged. Buck's mindless machismo clashes with Larry's effete sensibilities, and the two bicker terribly. Added to this the fact that neither of them has any great knowledge of history, they made a rather poor team together.
However, when they encounter Otto Osworth, an eight-year-old orphan who happens to be a history genius from the 21st century, he is quickly recruited and added to the team. Otto is shown to be the only one on the team with any enthusiasm or competence for the job. The problem is, neither of the other two are particularly willing to listen to his advice, and he must often resort to trickery to make sure the mission is completed.