The Byzantine empire lasted about eleven hundred years, and it was extremely vast. There were fourteen dynasties that ruled the empire. There were times when there was no dynasty as kings were overthrown, and no successor was to follow. The benefit with dynasties was that there was always a successor in place after the ruling king. This assured more stability and was a deterrent to internal strife and civil wars that weakens any empire or nation.
Such succession was uncontested and the emperors were careful to clarify which of his sons would rule the empire. There was continuity at numerous levels. There was continuity for policy and law which put the people at ease. Otherwise, the people of the empire would look to the new king each time to figure out how the laws of the land would change according to the whims of the new emperor.
Unlike the Roman Empire that leadership passed on from one generation to one generation of the same bloodline, most of the leaders of the Byzantine Empire were chosen by election. The first non-dynastic leader was Jovian, the Captain of the guards under the grandson of Constantius Chlorus, Julian where he was elected by the army when Julian died.
It was considered that Byzantine emperors were assigned by God to rule the empire. When the current emperor has a record of military defeats, ambitious military men used this to persuade the army to take over hence stopping the dynastic line and making them the newly appointed emperor. Most Byzantine emperors were from the military as they were considered capable of protecting their empire and people.