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.
Holy Roman Emperor
The Holy Roman Emperor was widely perceived to rule by divine right, though he often contradicted or rivaled the Pope, most notably during the Investiture controversy. 
In theory, the Holy Roman Emperor was "primus inter pares" (first among equals) among other Catholic monarchs. In practice, a Holy Roman Emperor was only as strong as his army and alliances, including marriage alliances, made him. There was never a Holy Roman Empress regnant, though women such as Theophanu and Maria Theresa of Austria served as de facto Empresses regnant.
Throughout its history, the position was viewed as a defender of the Roman Catholic faith. Until the Reformation, the Emperor elect ("imperator electus") was required to be crowned by the Pope before assuming the imperial title. Charles V, Holy Roman Emperor was the last to be crowned by the Pope in 1530. Even after the Reformation, the elected Emperor always was a Roman Catholic. There were short periods in history when the electoral college was dominated by Protestants, and the electors usually voted in their own political interest.