Are you wondering about the specific use as a formal title of power? Caesar means “Emperor” in Latin, and has many modern derivatives used into the 20th century such as German “Kaiser” and Russian “Czar”.

It’s use a a formal title bestowed on a Roman ruler ended after the Constantinian period, about 361.

However it was used sporadically up to the end of the Western Roman Empire in 476.

It was also adopted as a formality at times by the Byzantine and Ottoman Empires.

Edit: regarding Augustus... this was also an honorific and formal title meaning “Your Majesty”, and was used frequently as a superlative to “Caesar”. This was used as recently as Charlemagne in the Holy Roman Empire.