"I was supposed to fly to London, via Stockholm, with SAS," one passenger at Athens International Airport told Greek broadcaster Mega TV. "I'm working on Newport Hospital tomorrow morning. I'm not going to be there on time, I don't know what else to say.
"Who is going to pay for the additional cost this travel will cost me? We still don't know if and when we're going to leave, no one is telling us anything."
More than 90 flights have been affected in and out of Athens airport alone - though some flights have since been able to resume.
A member of staff in the airport told the BBC that 35 aircraft an hour were now being allowed to take off, but it was still unable to take inbound flights.
Flights departing from Dublin, Barcelona and Paris were earlier ordered to return to their airports of origin, while services from Copenhagen and Malta were cancelled altogether.
Other arrivals into Athens were placed on standby, while flights in and out of other Greek airports have also been affected. Three flights out of Heraklion airport on the island of Crete, including one to Munich, have been delayed, according to public broadcaster ERT.
Most inbound flights are being diverted to Turkey if not cancelled outright, it reports.