Phaselis is claimed to have been founded in 690 BC by Dorian colonists from Rhodos under the hero Lacius. Three natural harbours made it into one of the most important harbour cities along the Mediterranean. It had good trade relationships with Persia, which had its disadvantages, for one, it was never considered to be a fully Lycian city. In 333 BC Alexander the Great, accepting a golden crown, took hold of the town. Only in the second century was the city accepted into the Lycian Bond, its membership of that Bond was halted during 30 years of occupation by pirates. Most of what you see nowadays is from Roman times. The city flourished again in Byzantine times as a basis for the fleet.
I in vain tried to reach the acropolis, which the guide book promised would be hard anyhow. It also states the function of most of the buildings one can see is unknown. I identified some, though. For help I found the an excellent site. Please inform me if that link gets broken.