Heathrow is among several European airports hit by a cyber-attack affecting an electronic check-in and baggage system.
The airport warned of possible delays due to a technical issue affecting software provided by Collins Aerospace to several airlines.
Brussels Airport said a cyber-attack on Friday night meant passengers were being checked in and boarded manually, while Berlin's Brandenburg Airport also reported longer waiting times due to the problem.
RTX, which owns Collins Aerospace, said it was aware of a cyber-related disruption to its system in select airports and that it was working to resolve the issue as quickly as possible.
The company added: The impact is limited to electronic customer check-in and baggage drop and can be mitigated with manual check-in operations. It said the attack hit its Muse software - which allows different airlines to use the same check-in desks and boarding gates at an airport, rather than requiring their own.
The BBC understands that British Airways is operating as normal using a back-up system, but that most other airlines operating from Heathrow have been affected.
Hundreds of flights have been delayed at the airports throughout Saturday, according to flight tracker FlightAware.
Lucy Spencer said she had been queuing to check in for a Malaysia Airlines flight for more than two hours, and that staff were manually tagging luggage and checking passengers in over the phone.
They told us to use the boarding passes on our phone, but when we got to the gates they weren't working - they've now sent us back to the check-in gate, she told the BBC from Heathrow's Terminal 4, adding that she could see hundreds of people queuing up.
Another passenger, Monazza Aslam, said she had been sat on the tarmac for over an hour with no idea when we will fly, and had already missed her onward connection at Doha.
I've been at Heathrow with my elderly parents since 05:00, she said, adding: We are hungry and tired.
However, Luke Agger-Joynes said that while queues in Terminal 3 were much larger than normal, the airline for his US flight and the airport seem to be prepared and the queues are moving much faster than I feared.
Heathrow said additional staff were at hand in check-in areas to help minimize disruption.
Transport Secretary Heidi Alexander said she was aware of the incident and was getting regular updates and monitoring the situation.
EasyJet and Ryanair, which do not operate out of Heathrow but are among Europe's biggest airlines, said they were operating as normal.
Brussels Airport said there would be a large impact on the flight schedule, including cancellations and delays. Long queues and large crowds could be seen at the airport on Saturday morning.
Travel journalist Simon Calder said that any disruption is potentially serious at Heathrow, given it is Europe's busiest airport.
While there are unfounded accusations circulating that this cyber-attack was carried out by Kremlin-sponsored hackers, cyber-security experts suggest that this could be a ransomware attack, but note it could also be perpetrated by state-sponsored actors.
Collins Aerospace has yet to comment publicly about the nature or origin of the hack.