Aer Lingus says it's operating a normal schedule today.
In a statement, the company sincerely apologised for the severe disruption on Saturday.
The airline is advising customers impacted by the system outage to apply for a refund or change their travel plans, free of charge, through the 'manage booking' facility, call centres, and social media.
Travel expert Eoghan Corry has this advice for those trying to get in touch with Aer Lingus:
"So getting in touch with Aer Lingus, my strong advice is go to the webchat - which of course wasn't working on Saturday - and go through direct messaging.
"They're the two key ways to get in touch with an airline."