What do modern democracies have in commen with Athens?

Well, let's see ...

What is a democracy?

A democracy is a government type that is governed by the people. For example, the people vote upon each and every issue that comes up.

A republic is a government in which people elect representatives to a Council to represent them and to vote for them in these issues. Since people are usually very busy and cannot keep up with every nuance of politics, a republic is better prepared for issues. The USA is a republic, and not a democracy as most people proclaim. Rome was also a republic, and Greece was a democracy.

To explicitly answer your question, nothing has changed! The concept of a democracy has not changed in the course of history.

Democracy was founded in Athens!