Barad-dûr was built by Sauron, the Dark Lord of Mordor, with the power of the One Ring, during the Second Age. The building took six hundred years to complete; it was the greatest fortress ever built since the Fall of Angband, and much of Sauron's personal power went into it.
Barad-dûr was besieged for seven years by the Last Alliance of Elves and Men, and was levelled after Sauron's defeat at the end of the Second Age, but because it was created using the power of the One Ring its foundations could not be destroyed completely unless the Ring itself should be destroyed. Isildur cut the Ring from Sauron's hand but refused to destroy it, so the Tower was quickly re-built when Sauron returned to Mordor thousands of years later.
An interesting contradiction exists regarding the Dark Tower: Appendix B has Sauron beginning to build the Tower in c.1000 S.A., completing it at the same time he forges the One Ring c.1600 S.A., yet Elrond asserts that its foundations "were made with the power of the Ring." No explanation is offered in the text, but it appears that without the Ring's sustaining power the Tower's foundations provided insufficient support for the structure. Thus when the Ring was destroyed the Tower collapsed.
The Dark Tower was described as existing on a massive scale so large it was almost surreal, although Tolkien does not provide much detail beyond its size and immense strength. Since it had a "topmost tower" it presumably had multiple towers. It is otherwise described as dark and surrounded in shadow, so that it could not be clearly seen.
"..rising black, blacker and darker than the vast shades amid which it stood, the cruel pinnacles and iron crown of the topmost tower of Barad-dûr..."
In his vision at Amon Hen, Frodo Baggins perceived the immense tower as "wall upon wall, battlement upon battlement, black, immeasurably strong, mountain of iron, gate of steel, tower of adamant...Barad-dûr, Fortress of Sauron".
The Return of the King (film) also shows Barad-dûr as clearly visible from the Black Gate of Mordor. Even granting its enormous size, it was located one hundred miles away and to the east of the Gate, not to mention being behind the inner mountain ridges of Udûn so Aragorn's army would not have been able to see it. It is also shown in front of Mount Doom, but when looking from the gate as shown in the maps of Middle-earth, Barad-dûr is actually somewhat behind Mount Doom. In the film version, the geography of Mordor and Middle-earth in general seems to have been compressed somewhat, perhaps for artistic reasons related to rendering such complex stories in a visual medium. In the case of the Black Gate scene, having Barad-dûr visible from the Gate means that the army can see the Eye of Sauron staring at them. However, Jackson's literal interpretation of the Eye as Sauron's physical form is not found in Tolkien. In the books Sauron was never physically an Eye, and occupied a chamber inside the tower which had a window looking directly toward Mount Doom.
"Barad-dûr"