The Delta Quadrant was the common designation for one-quarter of the Milky Way Galaxy. This quadrant was adjacent to the Beta Quadrant and to the Gamma Quadrant. The quadrant's closest point to the United Federation of Planets was located in the galactic core, which was located approximately 30,000 light years away.
The Delta Quadrant was home to thousands of species, including the Kazon, Talaxians, Ocampans, Borg, Vidiians, Hirogen, Krenim, and many others.
Humans were first planted in the Delta Quadrant by a race known as the Briori around the year 1937 as a form of slave labor. The slaves rebelled and their descendants built a new civilization on a class L planet.
The Delta Quadrant was first visited by Humans of their own free will on stardate 32629.4, when the USS Raven followed a Borg vessel into a transwarp conduit. The first Starfleet mission into the Delta Quadrant occurred during an inspection of the Barzan wormhole in 2366.
Due to the considerable distance between the Alpha and Delta Quadrants (an Intrepid-class starship would take thirty years to reach the edges of the quadrant at its maximum warp velocity), the Federation knew very little about this region of space until 2371, when the starship USS Voyager was pulled into the quadrant by an alien force called the Caretaker. When contact was reestablished with the starship in 2374, hundreds of kiloquads of data on the region was received, increasing the Federation's knowledge of the quadrant immensely.
When Q discovered Voyager, he assumed Quinn (also a Q) was responsible for transporting it there, stating that Humans weren't supposed to be in the Delta Quadrant for another hundred years.
When Voyager returned to Earth from the Borg transwarp network in 2378, the Federation's knowledge of the quadrant was expanded considerably.