How was monarchy practice in ancient Greece?

classic monarchy, such as kings, vassals, so forth and so on, wasn't invented or even implemented in ancient Greece. greece was a republic, similar to how the US of A is today. they had a group that would make decisions, a republic, and this republic would rule over the land. it worked out quite well, until i believe the Romans took over. typing republic into google would give much better info on the republics than i could.