The first problem happened just after lunchtime Wednesday when a fire alarm forced the evacuation of the airport's control tower.
British Airways has apologised after IT issues caused dozens of flights in and out of Heathrow Airport to be cancelled, described by one passenger as "complete chaos".
Passengers at the airport on Wednesday were left frustrated as those trying to catch flights were faced with a lack of information and alternative travel options from the airline. It's not terribly helpful...
A spokeswoman for the National Air Traffic Services (NATS) said: "the control tower had been evacuated" after an alarm was triggered. They can't re-book the flights because they've got no computer system.
Passengers have also taken to social media to complain that departing flights have been stuck on the tarmac for more than an hour at Heathrow, while those due to arrive at the airport have also been diverted to Luton.
She added that flights are operating today, now the supplier "has resolved the issue", but didn't explain what the root cause was when IT Pro asked.
Virgin Atlantic said it is not affected by any IT issues at Heathrow.
"We are working with our supplier to resolve the matter and are sorry for the disruption to our customers' travel plans", British Airways said in a statement.
The failure is a blow as airlines gear up for the peak holiday period.