Roman emperor
The Western Roman Empire collapsed in the late 5th century. Romulus Augustulus is often considered to be the last emperor of the West after his forced abdication in 476, although Julius Nepos maintained a claim recognized by the Eastern Empire to the title until his death in 480. Following Nepos' death, the Eastern Emperor Zeno abolished the division of the position and proclaimed himself as the sole Emperor of a reunited Roman Empire. The Eastern imperial lineage continued to rule from Constantinople ("New Rome"); they continued to style themselves as Emperor of the Romans (later βασιλεύς Ῥωμαίων in Greek), but are often referred to in modern scholarship as Byzantine emperors. Constantine XI Palaiologos was the last Roman emperor in Constantinople, dying in the Fall of Constantinople to the Ottomans in 1453.
Byzantine Empire
A nephew of the last Emperor, Constantine XI, Andreas Palaiologos claimed to have inherited the title of Byzantine Emperor. He lived in the Morea until its fall in 1460, then escaped to Rome where he lived under the protection of the Papal States for the remainder of his life. Since the office of emperor had never been technically hereditary, Andreas' claim would have been without merit under Byzantine law. However, the Empire had vanished, and Western states generally followed the Roman-church-sanctioned principles of hereditary sovereignty. Seeking a life in the west, Andreas styled himself "Imperator Constantinopolitanus" ("Emperor of Constantinople"), and sold his succession rights to both Charles VIII of France and the Catholic Monarchs.