Underspace, also known as the Vaadwaur subspace corridors, was a network of subspace corridors in the Delta Quadrant that allowed starships to travel great distances in a matter of minutes. (ST reference: Star Charts)
Prior to the 15th century, the Vaadwaur spent 900 years mapping the corridors of Underspace, which took them as far as Talax and beyond. They used them at first for trading and exploration, but also to expand their empire by attacking undefended worlds at their pleasure. The Vaadwaur kept no written records of Underspace, rather keeping the information committed to their memory.
The Vaadwaur, however, lost control of Underspace when the Turei and a dozen other species rose up against them. After apparently destroying the Vaadwaur homeworld, the Turei took control of Underspace. Unfortunately, they did not have the Vaadwaur's knowledge as to how to maintain it.
In 2376, Underspace was discovered by the Federation starship USS Voyager when its warp field interacted with one of the corridors and it was pulled into Underspace. The Turei expelled them from the corridor with a resonance pulse, but then demanded to board Voyager to eliminate all evidence of Underspace, which would have involved completely wiping the memory of the ship's computer. Unwilling to resort to these measures, Voyager took shelter on the radioactive Vaadwaur homeworld, where they discovered a battalion of Vaadwaur who survived the war in stasis pods.
The Vaadwaur offered to cooperate with the Voyager crew and show them corridors of which the Turei have never been aware. However, their desire to regain their former power ultimately led them to attempt to capture Voyager and its advanced technology. Voyager defeated them with help from the Turei and the remaining Vaadwaur ships fled into Underspace. (VOY episode: "Dragon's Teeth")