There was no constitutional office of “Roman emperor” (the first person actually to bear that title was Mixahl I “Rhangabes” in the early 9th Century, who was styled Basileys Rhomaiôn, “Emperor of the Romans”), nor any title or rank directly analogous to the title of “emperor”; all the titles traditionally associated with the Emperor had pre-existing, Republican meanings. “Roman Emperor” is a convenient shorthand used by historians to express the much more complicated nature of being the “First Man” in the Roman state, and as a result there are many differing opinions as to precisely who was Emperor when, and how many Emperors there were.
The emperor’s legal authority derived from the extraordinary concentration of individual powers and offices extant in the Republic rather than from a new political office (emperors regularly had themselves elected to the consulate and the censorate); the emperor actually held the non-“imperial” offices of princeps senatus (parliamentary leader of the house in the Senate) and pontifex maximus (chief priest of the Roman state religion; lit. “greatest bridge-maker”), both of which had existed for hundreds of years before the Empire. (Gratianus was the last emperor to be pontifex maximus; he surrendered the pontificate maximus in 382 to Siricius and it permanently became an auxiliary honour of the Bishop of Rome.)
However, these offices only provided great dignitas (personal prestige) and auctoritas (influence or clout); the emperor’s powers derived from the fact that he held ad personam (i.e., without holding office) both imperium maius (supreme authority or command) and tribunicia potestas (tribunician power). As a result, he formally outranked the provincial governors and the ordinary magistrates (magistratus ordinarii), had the right to enact capital punishment, could command obedience of private citizens (privati), enjoyed personal inviolability (sacrosanctitas), could rescue any plebeian from the hands of any patrician magistrate (ius auxiliandi), and interpose his veto on any act or proposal of any magistrate, including the tribunes of the people (ius intercessio).
“Emperor” was not a magistracy or office of state (note that there was no formally prescribed “uniform” such as those of curule magistrates, senators, and knights; later emperors were distinguished by wearing togae purpurae, purple togas – hence the phrase “to don the purple” for the assumption of imperial dignity), nor was there even a regular title until the 3rd century. The titles customarily associated with the imperial dignity are imperator (“commander”, lit. “one who prepares against”), which emphasises the emperor’s military supremacy (later particularly ironical in the era of the so-called “Barracks Emperors”), caesar, which was originally a name but came to be used to refer to the designated heir (as Nobilissimus Caesar, “Most Noble Caesar”) and was retained upon accession, and augustus (“majestic” or “venerable”), which was adopted upon accession (the three titles were rendered in Greek as autokratôr, kaisar, and augustos (or sebastos), respectively). When Diocletianus established the Tetrarchy, caesar designated the two junior sub-emperors and augustus the two senior emperors.
The word princeps, from the emperor’s office of princeps senatus, was most commonly used to refer to the emperor in Latin (although the emperor’s actual constitutional position was essentially “pontifex maximus with tribunician power”); the Greek word basileys (“king”) was modified to be synonymous with princeps in the sense of “emperor” (and primarily came into favour after Heraclius defeated the Persian “Great King”, or basileys). In the era of Diocletianus and beyond, princeps fell into disuse and was replaced with dominus (“lord”); later emperors used the formula Imperator Caesar NN. Pius Felix (Invictus) Augustus. The use of princeps and dominus broadly symbolise the differences in the Empire’s government, giving rise to the era designations “Principate” and “Dominate”.
The line of Roman emperors in the East continues unbroken until the fall of Constantinople in 1453 under Konstantinos XI Palaeologos. These emperors eventually normalised the imperial dignity into the modern conception of an emperor, incorporated it into the constitutions of the state, and adopted the aforementioned title Basileys Rhomaiôn (“Emperor of the Romans”; these Emperors ceased to use Latin as the language of state after Heraclius). Historians have customarily treated these later Eastern emperors under the non-historical name “Byzantine Empire”.