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.
Western Roman Empire
The authority of Julius Nepos as Emperor was accepted not only by Odoacer in Italy, but by the Eastern Empire and Syagrius in Gaul (who had not recognized Romulus Augustulus). Nepos was murdered by his own soldiers in 480, a plot some attribute to Odoacer or the previous, deposed emperor Glycerius, and the Eastern Emperor Zeno chose not to appoint a new western emperor. Zeno, recognizing that no true Roman control remained over the territories legally governed by the Western court, instead chose to abolish the juridical division of the position of Emperor and declared himself the sole emperor of the Roman Empire. Zeno became the first sole Roman emperor since the division after Theodosius I, 85 years prior, and the position would never again be divided. As such, the (eastern) Roman emperors after 480 are the successors of the western ones, albeit only in a juridical sense. These emperors would continue to rule the Roman Empire until the Fall of Constantinople in 1453, nearly a thousand years later. As 480 marks the end of the juridical division of the empire into two separate imperial courts, some historians refer to the death of Nepos and abolition of the Western Empire by Zeno as the end of the Western Roman Empire.