Greece is a member state of the European Union and has ratified the Schengen Agreement. EU nationals traveling to Greece just need to display their national ID card without the need of a passport. Non-EU nationals traveling to Greece need a passport and possibly a visa. Further information can be obtained from the Hellenic Embassies or Consulates in their countries.
For updated info, refer also to the website of the European Union:
https://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-nationals/index_en.htm

Arrivals & Departures: for full details concerning currency declaration, alcohol, tobacco, animals & plants and restrictions of products of animal origin, refer to the website of the European Union:
https://europa.eu/youreurope/citizens/travel/index_en.htm