Before the shattering of Draenor, the Black Temple was once called the Temple of Karabor, a sacred site to the draenei which served as the refuge of the Prophet Velen. Shortly after the formation of the Horde, Gul'dan ordered the temple conquered and transformed it into the headquarters for the Shadow Council, renaming it the Black Temple in the process. It was later used as a fortress for the then-mortal Ner'zhul. In the trailer for the Black Temple, it shows the scene where Gul'dan's men attack the temple.
Sometime after the destruction of Draenor it was taken over by the Burning Legion. Renamed the Black Citadel, it was used as a "prime staging ground for the Burning Legion's campaign of destruction."
After Illidan conquered much of Outland, including the Black Temple, and following his defeat at the hands of Arthas Menethil, Illidan returned to the Black Temple where he resides to this day. Neither his activities nor mental state are known at this time. While Malfurion has stated that Illidan has become mad and delusional, believing that he killed Arthas and accomplished the mission Kil'jaeden had sent him on, it says on the Burning Crusade website that "Illidan lives in fear that he will be discovered by his powerful enemies — most notably Arthas, the new Lich King, and the remaining Lords of the Burning Legion." If Illidan has descended into madness and believes he accomplished his mission it would make no sense for him to worry about Arthas or Kil'jaeden coming after him; he would believe the former dead, and the latter appeased. But then again, those afflicted by madness rarely make sense.