Efforts are continuing to clear the backlog of flights after seven days of disruption caused by the volcanic ash cloud from Iceland.
Airlines are putting on extra flights to bring home thousands of Irish passengers left stranded abroad.
The advice to passengers is to confirm their booking before they travel to the airport and to expect delays.
Aer Lingus resumed a partial service yesterday afternoon and today the airline has confirmed that all its flights between Ireland and Britain, Europe and the US are scheduled to operate as normal.
Aer Lingus will also be carrying more passengers to parts of southern Europe where most people have been stuck for the past week.
Ryanair has said all its flights in northern Europe resumed this morning at 5am, with the exception of flights between Ireland and Britain, which will resume tomorrow at 5am.
The Irish Aviation Authority has warned it could take some days for full service to be restored.
Eurocontrol has said it expects air traffic to be 'almost 100%' today and estimated that 75% of the 28,000 flights scheduled for yesterday had flown.
All Europe's main air hubs were up and running by yesterday evening and experts in Iceland said the activity at Eyjafjallajokull volcano had lost most of its intensity.
It emerged today that during the period flights were grounded a record 72,000 passengers travelled on ferries through Dublin Port.
O'Leary 'got it wrong'
Separately, Ryanair says it will comply with European regulations under which EU airlines are required to reimburse the reasonable receipted expenses of disrupted passengers.
Ryanair spokesperson Stephen McNamara says Chief Executive Michael O'Leary 'got it wrong' when he said the airline would limit its refunds to stranded passengers.
The airline today said it was happy to work within the EU regulations, which allow passengers to claim reasonable expenses.
Extra staff have been drafted in to deal with the expenses claims.
Passengers are asked to send in copies of their receipts when they return home.
It is hoped that they will be refunded within a number of weeks.
In a statement this morning, Mr O'Leary said: 'The events of the last seven days, under which Europe's airlines were prevented from flying by the closure of European airspace highlight how absurd and discriminatory the EU261 regulations are towards Europe's airlines.'
The Commission for Aviation Regulation has said that there is scope for a review of EU legislation allowing passengers claim reimbursements from airlines.
Patricia Barton of the Commission for Aviation Regulation said however that law is the law and airlines cannot opt-out of legislation when it suits.
The CER has also said, however, that there is scope for a review of the law.
Passengers intending to claim expenses incurred as a result of the travel disruption are being advised to contact the Commission for Aviation Regulation.
