(covers information from several alternate timelines)
Tholian space was the territorial region of space claimed by the Tholian Assembly.
The border to the space annexed by the Tholian Assembly was located in free space that had not yet been surveyed by the United Federation of Planets in 2268. (TOS: "The Tholian Web")
Mirror universe[]
In the 2150s of the mirror universe, the Tholians were known to frequently annex star systems outside their core territory.
In 2155, the Tholians, having lured the USS Defiant from 2268 of the prime universe through an interphasic rift, kept the ship within a small moon drydock in the Vintaak system, deep in Tholian space. Commander Jonathan Archer of Starfleet learned of the vessel's presence in his universe. When Captain Maximilian Forrest refused to take ISS Enterprise into Tholian space, Archer commandeered the ship and flew it in, while cloaked, to acquire the Defiant.
Though Forrest soon took back the bridge, T'Pol was unable to fulfill his order to take Enterprise out of Tholian space at maximum warp as Archer revealed that autonavigation could not be released until they reached the coordinates he had set. Receiving orders from Fleet Admiral Gardner forcing him to investigate the Defiant, Forrest assigned Archer as the leader of an assault team which would board the Defiant where they were to destroy the ship after downloading whatever they could from its database. Though Archer protested that they should take the Defiant with them, Forrest insisted that it was too dangerous as they were deep in Tholian space. However, after Archer sent a team to the Defiant, the Tholians spun a web around Enterprise and destroyed it. Soon after, the team managed to activate the Defiant's systems and escape the system after destroying the drydock and three Tholian ships. (ENT: "In a Mirror, Darkly", "In a Mirror, Darkly, Part II")