While searching for Eli Whitney, the time cop Buck Tuddrussel and his robot partner, the Larry 3000, end up at an orphanage in 2001 where they discover an orphaned history buff named Otto Osworth and take him with them to complete their mission.
The Time Squad travels to Ancient Greece, where it is the King of Troy's birthday. The Greek army brings the fabled Trojan Horse to the festivities, but fails to realize that it is supposed to be a trap, not an actual gift.
The Time Squad gets sentenced to the guillotine when it ends up in 18th century France, and Tuddrussel mistakes the diminutive leader for a child. Things get more complicated when it's revealed that Napoleon's wife is nagging him around and Napoleon is too cowardly to stop her.
After Otto and Tuddrussel accidentally smash a hole in the Domisphere (and try to cover it up from Larry), the Time Squad visits Robin Hood, who is stealing from the poor and giving to the rich instead of robbing from the rich and giving to the poor.
The Time Squad gets sent to the time of the great musician Ludwig van Beethoven, who is now a pro-wrestler fighting other classical musicians turned wrestlers — and Tuddrussel challenges Beethoven to a match to preserve the dignity of pro-wrestling.
After being upset with grumpy Tuddrussel, (who just wants a cup of coffee), Larry is delighted to discover that instead of dumping tea into the Boston Harbor, the Sons of Liberty are having civilized tea parties. Tuddrussel and Otto have to convince them into dumping the overtaxed colonial beverage for the sake of all America. To do that they must use coffee.
The Time Squad finishes a relatively easy assignment in helping Nicolaus Copernicus become an astronomer instead of a farmer, but the crew ends up waiting until the Larry 3000 can restart his time travel software in order for them to go home. After they finally leave, Copernicus realizes that he knows nothing about astronomy.