The Turei were a spacefaring culture from the Delta Quadrant. In the late 24th century, they were the keepers of the underspace corridors that traversed the Delta Quadrant. This underspace was once the property of the Vaadwaur, but in 1484 the Turei led an alliance of the Vaadwaur's enemies, launching a massive orbital assault on the Vaadwaur homeworld.
With the Vaadwaur apparently defeated, the Turei maintained their control over the underspace until 2376 when the USS Voyager accidentally entered it. Unable to escape from it, Voyager passed a Turei starship which forced Voyager back in to normal space. The Turei then demanded that they be allowed to board Voyager in order to remove all data on the underspace. When Captain Janeway refused, the Turei pursued Voyager to the Vaadwaur homeworld. Voyager entered the planet's atmosphere, which was still irradiated centuries after the bombardment, Voyager' shields being better equipped to cope with the radiation than the Turei ships were.
Voyager's crew discovered and revived those Vaadwaur who had entered into stasis prior to the Turei attack. These Vaadwaur quickly proved themselves to be treacherous, and attempted to overtake Voyager. However, with help from the Turei, Voyager was able to escape. (VOY: "Dragon's Teeth")
According to the script, this species was identified as "Turei Tunnel Dwellers", further explaining that "This is a species that lives in the subspace corridors."
According to a deleted line from the episode, they were given the Borg species designation of "Species 532".
In the Delta Rising expansion to Star Trek Online, the Vaadwaur attack the Turei homeworld in 2410, attempting to regain control of underspace. The Voth, longtime allies of the Turei, attempt to fight them off, but it takes the arrival of the player character to tip the battle in the Turei's favor.