Barad-dûr ('Dark Tower') is the fortress of Sauron "above the valley of Gorgoroth"1 in the land of Mordor in J.R.R. Tolkien's Middle-Earth.
In The Two Towers, Aragorn states that "the Orcs in the service of Barad-dûr use the sign of the Red Eye (Sauron's emblem)."
It is recorded in The Silmarillion that "in the days of Tar-Minaster, the eleventh King of Númenor, [Sauron] had fortified the land of Mordor and had built there the Tower of Barad-dûr. (circa 1000, Second Age [SA])"
At the end of the Second Age, Gil-galad and Elendil lay seige to Barad-dûr (3434-3441 SA), eventually defeating Sauron and razing the Dark Tower.
In the year 2951 of the Third Age (TA) Sauron "begins the rebuilding of Barad-dûr."2
In the year 3017 TA, Gollum is captured and taken to Barad-dûr to be questioned by Sauron as to the whereabouts of the One Ring.3
In The Return of the King, Frodo destroys the Ring (March 25, 3019 TA), thus sealing the "downfall of Barad-dûr and the passing of Sauron."
1 The Silmarillion
2 The Return of the King, Appendix B
3 Unfinished Tales, The Hunt for the Ring