Note: It is difficult to determine when exactly the Roman Empire ends and the Byzantine Empire begins; Diocletian split the Roman Empire into eastern and western halves for administrative purposes in 284. Candidates for the "first" Byzantine emperor include Constantine I (the first Christian emperor, who moved the capital to Constantinople), Valens (the Battle of Adrianople (378) provides one of the traditional cut-off events to mark the start of the medieval period), Arcadius (treating Theodosius I as the last emperor of a single Roman Empire), and Zeno I (as the last western emperor Romulus Augustus was deposed during his reign). Others date the beginning of the Empire even as late as Heraclius (who replaced the traditional Roman imperial title of "Augustus" with "Basileus", the Greek word for "Emperor", and discontinued the use of Latin by making Greek the official language). Numismatists note the monetary reforms of Anastasius I in 498, which used the Greek numbering system. Of course, the Byzantines themselves continued to think of their empire as "Roman" for over a millennium.
Julian the Apostate (331 - 363, ruled 361 - 363) – son in-law of Constantine I, brother-in-law and first cousin of Constantius II, grandson of Constantius I
Justinian I the Great (482-565, ruled 527 - 565) – nephew of Justin I
Justin II (520-578, ruled 565 - 578) – nephew of Justinian I
Tiberius II Constantine (540-582, ruled 578 - 582) – father-in-law of a grand-nephew of Justin I; Count of the Excubitors under Justin II; adopted by Justin II in 574
Maurice I Tiberius (539-602, ruled 582 - 602) – son-in-law of Tiberius II
Non-dynastic
Phocas the Tyrant (???-610, ruled 602 - 610) – overthrew Maurice
Nicephorus III Botaniates (1001-1081, ruled 1078 - 1081) – married Michael VII's wife Maria of Alania (Maria was accused of bigamy as Michael was still alive)
Alexius I Comnenus (1057-1118, ruled 1081 - 1118) – nephew of Isaac I; married Constantine X's grandniece
Andronicus I Comnenus (1118-1185, ruled 1183 - 1185) – grandson of Alexius I; nephew of John II; first cousin once removed of Alexius II; married Alexius II's widow
Constantine XI Palaeologus (1405-1453, ruled 1449 - 1453) – son of Manuel II, brother of John VIII
In 1453 Mehmed II overthrew the Byzantine Empire and claimed the title of Caesar; his successors continued this claim. See Osmanli for the complete list of Ottoman sultans.