The Dark Tower was another name for Barad-Dûr, and the common speech equivalent, from 'barad' - tower and 'dûr' - dark.

The Dark Tower was Sauron's stronghold, built over 600 years from 1000 S.A. to 1600 S.A. from iron, hard stone and steel. He looked out on the world from a window atop the highest tower - the Window of the Eye.

The Dark Tower was Sauron's home for much of the Second and Third Ages, and we may assume that he was at the Window of the Eye when it collapsed during the destruction of Mordor and his fall on the 25th of March, TA 3019. It was never rebuilt, and was abandoned.
Encyclopedia entry originally written by Simbelmyne