As of 25 May a couple of measurements have been loosened in Greece. The first this is apparent in the catering: outside terraces have been reopend. Also it’s possible to travel to and from the islands.
As of 1 June the year-round hotels and campings are allowed to open.
As of 15 June the seasonal hotels/resorts will be allowed to open and flights from abroad will be allowed from countries ‘with good epidemiological features’ (not mentioned who these are) on Athens.
As of 1 July flights to all Greek airports and from all countries will start, with the exception of those presenting negative epidemiological features (supposedly they’ll announce later who these are).
For the entrance of visitors in Greece, there will be no condition of any type of test or the imposition of any quarantine, while only sample tests for epidemiological monitoring will be applied.
For information see the official website of the Greek Ministry of Tourism: http://www.visitgreece.gr/en/home/about_covid_19.