In the Star Trek universe, the Beta Quadrant is 1/4 of the Milky Way, usually shown in the lower-right on maps of the galaxy.
The bulk of the Klingon and Romulan empires, as well as the Tholians are among the major cultures located here. The Federation extends a bit into the Beta Quadrant, though it is contained mostly within the Alpha Quadrant. Planets in the beta quadrant include Andoria, Qo'noS, Risa, Romulus, and Remus.