Morgoth descended into Arda at its beginning, and battled with the Valar for ages uncounted before the awakening of Elves and Men from his fortress at Utumno in the north of the world. The Valar defeated him and imprisoned him for three ages, but on his release he returned to Angband, north of Beleriand. During the First Age, the Noldor made hopeless war upon him for the return of the Silmarils, but at last the Valar came to their aid and overthrew Morgoth, banishing him forever from the World.
Sauron was the ancient lieutenant of Morgoth, and after the first Dark Lord's defeat, he took on his mantle and became a Dark Lord himself during the early Second Age. Taking the land of Mordor to dwell in, he corrupted the Númenóreans. Though he was defeated at the end of the Second Age, and his Dark Tower of Barad-dûr was thrown down, he rose again during the Third Age, and was finally defeated with the destruction of the One Ring in Third Age 3019.