Ancient Greece's (Athens) democracy is definitely one of the things they are most famous for. They let their people vote for their leaders and vote for the outcome of said leaders' decisions. The Athenians were concerned with the question who should lead and how they should lead, so having this kind of government was very important to them. Except, no matter how much they are famed for it, no part of Greece was a complete democracy as there were still many cases of unjustness like the allowance off slavery and women not being able to vote.
Ancient Greece's governments are very well known for their achievements and contributions both then and now. They're Athenian government even carried on from civilization to civilization and is still relevant and visible in our government system today. In fact, ancient Greece, specifically Athens, is considered the birthplace of one of their most well known achievements, democracy.
Though, a democracy wasn't their only type of government. On the other hand they had other types of governments too, like a tyranny, monarchy, and even an oligarchy, these types being more prominent to Sparta. These governments had their leaders play much bigger roles in running the country, as only people with positions could make decisions in these other governments. These leaders completely called the shots and were usually chosen by some kind of council or was a descendant of the former leader.(aside from tyranny).
Sparta was a mixture of a oligarchy and a monarchy, this is due to the fact that they had two hereditary kings ruling their people. They also had plenty of other groups of leaders that flew above the social ladder. These leaders were more militaristic and won many battles for Sparta. Except they didn't exactly have the best choice of leaders as they had no representation of the much lower class and did not allow women to have government positions.
However, Athens wasn't innocent either. Even through their famed democracy, their government was incredibly flawed. Similar to Sparta, Athens also allowed slavery, many households having at least three slaves each. Not to mention the extreme misogyny in Athens. It was more of a democracy for men than it was women or lower class people, as these oppressed groups were not allowed many rights and could not participate or vote in any government activities.
Though luckily, the better part of Athens' democracy was the part that got passed on throughout the generations and made it to the our modern world. We took their ideas and ways of effective leadership and improved it. They're government was the origin of most of the world's governments today, influencing many of our practices now and how our current system, laws, and rights work. Now, because of them, we have a better, more just government that works alongside its people to improve its country.