History of the Roman Empire
Theodosius was the last Emperor who ruled over the whole Empire. After his death in 395, he gave the two halves of the Empire to his two sons Arcadius and Honorius; Arcadius became ruler in the East, with his capital in Constantinople, and Honorius became ruler in the West, with his capital in Milan and later Ravenna. The Roman state would continue to have two different emperors with different seats of power throughout the 5th century, though the Eastern Romans considered themselves to be the only ones who were fully Roman. Latin was used in official writings as much as, if not more than, Greek and the two halves were nominally, culturally and historically, if not politically, the same state.
Roman emperor
This line of Roman emperors was actually generally Germanic rather than Roman, but maintained their Roman-ness as a matter of principle. These emperors used a variety of titles (most frequently ""Imperator Augustus"") before finally settling on "Imperator Romanus Electus" ("Elected Roman Emperor"). Historians customarily assign them the title "Holy Roman Emperor", which has a basis in actual historical usage, and treat their "Holy Roman Empire" as a separate institution. To Latin Catholics of the time, the Pope was the temporal authority as well as spiritual authority, and as Bishop of Rome he was recognized as having the power to anoint or crown a new Roman emperor. The last man to be crowned by the pope (although in Bologna, not Rome) was Charles V. All his successors bore only a title of "Elected Roman Emperor".