(coexisting on another dimensional plane)
The Terran Empire rebellion was a war fought between the Terran Empire and members of a rebellion comprised of conquered slave races in the 22nd and 23rd centuries. The Resistance included at least some Andorians, Tellarites, Vulcans, and Orions, and later also Klingons.
By January 2155, the war was going badly for Starfleet. Twelve ships had been lost in a recent battle at Tau Ceti, though Terran propaganda stated that the battle had gone well. It was projected that the war could be lost altogether in a matter of weeks.
It was against this backdrop that Commander Jonathan Archer of the ISS Enterprise received word through his contacts that a Terran vessel, reportedly from the future of a parallel universe, had been captured by the Tholian Assembly. After unsuccessfully trying to persuade Captain Maximilian Forrest to divert Enterprise to Tholian space to investigate rather than rendezvousing with Admiral Black's assault fleet as ordered, Archer staged a mutiny and locked Enterprise on a course to the Vintaak system, where the future vessel was being held. He then had his information on the vessel to Fleet Admiral Gardner, which turned out to be a fortuitous decision when Forrest regained his command with the help of Archer's first officer, Commander T'Pol.
Now with official orders from Gardner, Enterprise entered the Vintaak system (using a Suliban cloaking device to sneak past the Tholian patrols) and beamed over an assault team to the future vessel, the Constitution-class USS Defiant, that was being gutted in an asteroid drydock at the time. While they powered up the Defiant, Enterprise was eventually detected by several patrol ships and trapped inside a Tholian web. Enterprise was destroyed in the ensuing battle, but not before several escape pods escaped the ship with roughly half the crew. These pods were recovered by the Defiant once it broke free from the drydock and destroyed the Tholian ships.
With a crew of only 47, along with several alien slaves the Tholians had been using to disassemble the starship, Archer ordered the Defiant to rendezvous with Black's assault fleet. There were delayed due to sabotage from the Gorn slavemaster Slar, who was eventually captured and killed by Archer and several MACOs.
Meanwhile, a massive rebel force attacked the assault fleet. By the time Defiant arrived, only Black's flagship, the ISS Avenger, remained. The Defiant quickly made short work of three rebel ships (one Andorian battle cruiser, a Tellarite cruiser, and a Vulcan D'kyr-type. The lone remaining rebel ship (an Andorian battle cruiser) was allowed to flee, to spread word of the Defiant's overwhelming power.
In a speech to the crew of both the Defiant and the Avenger, after killing Admiral Black for trying to take his command, Archer laid out his plan to take the Defiant to Earth and overthrow the Emperor and the rest of the "corrupt and arrogant criminals" at Starfleet Command. However, T'Pol, Phlox, and Soval – afraid that Archer's xenophobia would make the Empire even more brutal towards non-Terrans than it already was – attempted to stop Archer by having Phlox sabotage the Defiant while the Avenger attempted to destroy it. Their plan was foiled by Chief engineer Tucker, and Avenger was destroyed with all hands.
Archer himself was shortly removed as well by his consort Hoshi Sato, with the help of Archer's bodyguard Travis Mayweather. When the Defiant arrived at Earth, "Empress" Sato demand that Starfleet surrender, or be destroyed. (ENT: "In a Mirror, Darkly", "In a Mirror, Darkly, Part II")
In the early 23rd century, rebels were successful in stealing information concerning the origin of the Defiant from Imperial computers. The data was then stored in a computer core aboard a Klingon vessel. (DIS: "Despite Yourself")
Despite the rebellion's early successes, the Terran Empire ultimately survived well into the late 23rd century. As of late 2256 or early 2257, the Empire, now controlling all of known space, was still combating rebel groups consisting of Vulcans, Andorians, Tellarites, and Klingons, among other races. (DIS: "Despite Yourself")
In the face of Imperial aggressions, two former enemies, the Klingons and the Cardassians formed a Klingon-Cardassian Alliance. Eventually the Empire underwent some pacifistic reforms by Spock, leaving it vulnerable against the hostile forces around it. The Alliance found an opportunity to strike against the Empire and succeeded it as a dominant power in the Alpha Quadrant throughout most of the 24th century. (DS9: "Through the Looking Glass")