Ancient Greece Monarchy
Monarchy - supreme power/sovereignty held by one person
How Ancient Greek Monarchies Functioned
Monarchies in ancient Greece weren't too common, and it was hard to distinguish that from a tyranny. Two Greek states known to have had a monarchy are Macedonia and Epeiros. Both states had a ruler that shared power with an assembly. Sparta, although not technically a monarchy, is famous for having two kings who were kept in check by ephors during peacetime. During time of war, the two kings held complete power over the Spartan army. Spartan kings were also part of the gerousia, and were admitted when they were young when other men couldn't join until they were 60. Even though the Spartan kings were rulers, they could still be put to trial, and even exiled.
Greek Monarchy Influence on Current Monarchies
Monarchies did not originate from Greece, so I wouldn't say it influences modern-day monarchies very much, but the general idea of having one leader is still here today.