Thousands of air passengers have been suffering long delays and cancellations after a "technical issue" hit UK air traffic control systems.
People are stuck in the UK and abroad after National Air Traffic Services limited the number of planes landing.
Airlines and airports warned there were still "significant delays" despite the issue being fixed within hours.
One passenger told BBC News her afternoon flight was not expected to leave until after midnight.
There have been warnings that some knock-on disruption could last for days.
Heathrow said late on Monday evening that schedules remained significantly disrupted, adding that people travelling on Tuesday should contact their airline before heading to the airport.
Gatwick Airport said it was planning to operate a normal schedule on Tuesday, but advised passengers to check the status of their flight with their airline before going to the airport.
London Luton Airport also said on Monday evening that flights across UK airspace remained subject to delays and cancellation, and people should check with their airline for the status of their flight.
Nats confirmed the fault just after midday on Monday before it announced at 15:15 BST that it had identified and remedied the issue.
It said, "It will take some time for flights to return to normal".
Several UK airports and airlines including British Airways, Virgin Atlantic and TUI, were hit by delays and cancellations on Monday.
BA said that there were "significant and unavoidable delays and cancellations" and apologised for the inconvenience caused.
It has advised customers who were travelling on short-haul services to check their flight was still running before heading to the airport.
The airline added customers due to travel on Monday and Tuesday may be able to move their flights free of charge to a later date.
Ryanair said it had been forced to delay or cancel some flights, and Jet2 said significant delays were expected on all of its flights to and from the UK.
It said passengers for flights on Tuesday should travel to the airport as normal unless otherwise advised.
Aviation analyst Sally Gethin said the disruption in the aftermath of the technical fault will last for days.
"Airlines will have a major headache now, looking after customers and getting the planes back to some normal schedule again," she told BBC News.
"I think we are going to see sizable disruption in the coming hours and tomorrow, and I think for some people there could be a knock-on effect into later this week."
Passengers recounted how they faced huge disruption as air traffic control effectively ground to a halt.
Serena Hamilton at Belfast International Airport said she was likely to miss a heart transplant check-up after her flight to Newcastle-upon-Tyne got cancelled.
"I had a transplant 15 months ago and these appointments are very important," she told BBC News.
Irene Franklin, 60, said she, her daughter, son-in-law and friends were forced to pay for a hotel after their Delta flight from Heathrow to Texas was cancelled at the last minute.
"It was [saying delayed by] two hours, now it's cancelled. It's now not until tomorrow morning at 10," she said.
Daniela Walther said she was supposed to catch a flight from Heathrow for Stuttgart, Germany, at 17:25, but it is now set to leave later than 01:00.
She added: "I know it's going to be long but on the other hand I don't dare to leave because I don't want to miss information, and I don't know if I don't get it on my phone."
Cricket journalist Rory Dollard said he and his family face being stuck in France for up to six days after his Ryanair flight was cancelled.
The father, from Skipton, North Yorkshire, is stuck at an airport in Bergerac with his wife and children, aged 10 and eight.
Thousands of flights affected
Cirium, an aviation data firm, said 3,049 flights would have been due to depart from UK airports on Monday, and a further 3,054 flights scheduled to arrive.
As of 14:30 BST its data showed that 232 departing fights had been cancelled, which it said was equivalent to 8% of all departures, and 271, or 9%, of incoming flights.
Transport Secretary Mark Harper advised "passengers should contact their airline for up-to-date flight information" and said he would encourage passengers to read the UK Civil Aviation Authority guidance to be aware of their rights when flights are delayed or cancelled.
The CAA says that an airline has a duty of care to provide food, drink and accommodation if delays stretch overnight.
If a flight is cancelled, passengers should be offered a choice of a refund or alternative travel arrangements at the earlier opportunity.
The air traffic control failure set off calls from the Liberal Democrats for the prime minister to convene emergency response committee Cobra, while Labour said the incident was "extremely concerning".
Nats said it was a "flight planning issue" which had affected the system's ability to automatically process flight plans.
This meant "that flight plans had to be processed manually which cannot be done at the same volume, hence the requirement for traffic flow restrictions".
Operations director Juliet Kennedy apologised for the disruption and announced an investigation into what happened.
Graham Lake, an aviation strategy consultant, told BBC Radio 4 PM: "What we have is a system failure that's caused a revert to a manual system [that] has a much lower capacity for processing aircraft, and so the only way you can keep it safe is to stop aircraft taking off.
"You can't stop the ones that are already airborne, but you stop the ones still on the ground until you've identified and remedied the fault."
He said the technical fault was "extremely rare", with the last one being in 2014.
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