It's hoped Dublin airport will today be able to clear the backlog of flights that were disrupted yesterday following a technical problem at an air traffic control centre in England.
The issue was resolved last night, but hundreds of flights were delayed and cancelled as a result.
However, many airports are reporting that they've returned to normal service today.
Dozens of passengers were forced to spend the night in airports.
The British National Air Traffic Service (Nats) is investigating the glitch which it said was fixed at 7.30pm on Saturday night.
The firm said the computerised telephone system, which air traffic controllers use to handle flights, failed to switch correctly from night time to day time mode.
It meant they had to carry out the process manually, leading to 8% of all air traffic in Europe - around 1,300 flights - being delayed.
Victoria Bacon from a British travel association, says most passengers won't be entitled to compensation because it's not the airlines' fault.
Ryanair called for action to prevent it happening again.
In a statement, the airline said: "Ryanair is calling on the Civil Aviation Authority to intervene and prevent further chaos for thousands of passengers affected by this ATC failure. While we acknowledge problems can occur, where is the contingency? It's simply not good enough and the CAA needs to act now."