British Airways has apologised to passengers facing delays after an IT glitch affected check-in desks.
Passengers complained of delays at check-in and at the baggage drop, and on the tarmac waiting for take-off.
"We are sorry for the delay to their journeys," BA added.
There was further disruption for passengers at London City Airport on Tuesday after, police said, protesters "locked themselves together" on the runway.
BA encouraged customers affected by the IT problems to check in online before they reached the airport. It told customers that some flights had been cancelled on Monday "due to operational reasons" but that specialists were "working to resolve this issue".
One passenger, Dana Al-Qatami, who was flying from Switzerland to London, was issued with a handwritten boarding pass on Tuesday morning.
Dana, alongside another Twitter user, Susan Stewart, said the delays continued once on the plane.
Ms Stewart, a director at the Open University in Scotland, tweeted: "Dear @British_Airways, could you turn the wifi BA 2953 please so we can work whilst stuck here on tarmac? (or let us off?)".
Liv Boeree, a professional poker player from London, told the BBC she had queued for a flight in Las Vegas for two and a half hours.
"It's now midnight and we are boarding. Check-in was long and slow. The staff handled it very well," she said.
"My boarding pass was filled out by hand. Even had a hand-written hand baggage label. Staff were updating us well - The staff... were excellent. The pilot said the delays were due to a computer glitch and apologised profusely."
On Monday customers in the US and Canada reported delays at several airports due to IT problems.
People flying from San Francisco, Washington DC and Atlanta reported long delays on social media.
Twitter user John Bevir wrote: "Huge computer issue affecting British Airways across USA. Friend at #Dulles [Washington airport] tells me pilots by gate but passengers still trying to check in!".
Ewan Crawford, of Glasgow, said he was at Chicago O'Hare International Airport. He tweeted: "Never a good sign when they deliver water to the gate! Waiting at ORD for @British-Airways 296. Worldwide computer outage apparently! Hmm."
Matthew Walker, a financial analyst from London, waited for more than two hours to board his flight to Heathrow.
Though he had already checked in online, he said that BA staff could not access their computers to see which passengers had gone through security.
He said: "People were lining up, some had already checked in and got through security, but others, when this thing happened, whatever it is, were stuck in the check-in queue.
"So they (the staff) have the problem that they didn't know who had already gone through the gate because all the systems literally just had a meltdown."
In July, British Airways apologised to passengers who faced long delays at check-in at Heathrow and Gatwick.
The airline was upgrading its check-in system and problems led to lengthy queues on one of the busiest days of the year for the airports.