Well, we got our political system from the Romans, they had a senate that voted on what to do with a head tribune that controlled the senate. We have a senate with a president that can do similar stuff as a tribune did. Also Romans had laws to keep the citizens in check like taxing the rich more and laying down the foundation to a civilization... For greeks I'm not to sure on we got, but for mathematics I know the greeks helped us with that like pie and other theorems also with space and stars the greeks helped us with that as well... So lots of stuff is still here from the ancient world. The most important would be the Roman contribution to their politics which has helped us run our country accordingly.
