The plans for Greece’s reopening to tourists

In the European Union Greece is moving the quickest, but still this does not sound so appealing:

Phase 1 – Until 15 June
International flights are allowed only into Athens airport.
All visitors are tested upon arrival and are required to stay overnight at a designated hotel. If the test is negative, then the passenger self-quarantines for 7 days. If the test is positive, the passenger is quarantined under supervision for 14 days.

Phase 2 – Bridge phase- 15 June to 30 June
International flights are allowed into Athens and Thessaloniki airports.
If your travel originated from an airport not in the EASA affected area list (https://www.easa.europa.eu/SD-2020-01/Airports#group-easa-downloads), then you are only subject to random tests upon arrival.
If you originate from an airport on the EASA affected area list, then you will be tested upon arrival. An overnight stay at a designated hotel is required. If the test is negative then the passenger self-quarantines for 7 days. If the test is positive, the passenger is quarantined under supervision for 14 days.

Here is much more detail.  Via Yannikouts.