The Black Pits were dungeons of torment located beneath the tower of Barad-dûr.
Between the years T.A. 3009 and T.A. 3017 of the Third Age, Gollum was held captive in the Black Pits, only being taken out to be interrogated. It is possible that he was interrogated by the Questioner. Gollum was released from the Black Pits only after he revealed the information that "Baggins" from "Shire" held the One Ring.
On 14 March of the year T.A. 3019, the Captain of the Tower of Cirith Ungol, Shagrat, cursed "that filthy rebel Gorbag" to the Black Pits after a skirmish broke out between his Orcs and Gorbag's company from Minas Morgul.
When Shagrat's underling, Snaga, informed him that he was not willing to report the happenings in the Tower to Sauron at Barad-dûr, Shagrat told him that they both would "be for the Black Pits" if such news would not get through to Sauron.