Gatwick's runway has reopened after drones caused the airport to shut down for more than a day.
The airport, the UK's second busiest, said 837 flights were scheduled but there were delays and cancellations.
Boss Chris Woodroofe said "mitigating measures" from the government and military had given him "confidence to reopen".
The drone operator is still at large and police said it was possible they were an environmental activist.
The airport is expected to be "back to normal" by the end of Saturday.
Thousands of passengers - including some attending funerals, honeymoons and Christmas reunions with their families - remain stranded at Gatwick.
The airport could not operate while the drones were in flight in case they hit and damaged a plane.
What is happening today?
Gatwick said the 837 flights planned for Friday would have more than 130,000 passengers on board.
A total of 155 flights have been cancelled.
Pilots' union Balpa said it understood detection and tracking equipment had been installed around Gatwick's perimeter and that if the drones reappear the airport would close again.
Mr Woodroofe said: "Additional mitigating measures provided by government agencies and military have given me the confidence to reopen the airport.
"We are now operating at almost normal runway conditions but the challenge for the airlines, as the result of this disruption, is that their planes are not all in the right place.
"So what we'll be doing today is recovering their operations so by tomorrow we are back to standard operation and continue to recover the situation for our passengers."
He added he was determined to get passengers moving so "they can enjoy their Christmas".
The first flights in and out of Gatwick were Norwegian Air, Easyjet and BA departures and a China Eastern Airlines arrival from Shanghai.
Staff continue to advise passengers to check their flight status before turning up at the airport.
Ryanair said it was switching all of its Gatwick flights to operate in and out of Stansted airport on Friday.
The police operation
Sussex Police was locked in a game of cat and mouse with the drone operator.
Officers have so far failed to locate the "industrial specification" drones or their pilot and had been considering plans to shoot a device down.
But Steve Barry, Sussex assistant chief constable, said they were in a "much better position today".
Mr Barry said a drone had last been seen at 22:00 GMT on Thursday.
He added measures to tackle the threat include "technical, sophisticated options to detect and mitigate drone incursions, all the way down to less sophisticated options" including using shotguns.
Mr Barry previously told BBC Breakfast there were a "number of lines of inquiry" into the "very malicious and criminal behaviour", including the possibility it could have been the work of an environmental activist.
At a press conference, he said there was "no evidence" the use of the drones was state-sponsored.
What does the government say?
Transport Secretary Chris Grayling said there was no evidence it was terror-related.
But he called it a type of disruption "we've not seen before" and "lessons need to be learned".
He said the situation was "unprecedented, anywhere in the world".
"Every possible measure will be put in place to make sure this can't happen again," he said.
But he added there was "no simple solution" and "you can't fire weapons haphazardly around an airport".
It is illegal to fly a drone within 1km of an airport or airfield boundary and flying above 400ft (120m) - which increases the risk of a collision with a manned aircraft - is also banned.
Endangering the safety of an aircraft is a criminal offence which can carry a prison sentence of five years.
At the scene: Tom Pugh, BBC South East reporter
At Gatwick Airport's South Terminal this morning, passengers waited anxiously for news on whether their flights would depart.
It appears to be much quieter here today, compared to the chaotic scenes yesterday.
As the West Sussex airport announced the reopening of its runway on Friday, some travellers were hopeful of getting airborne.
But others expressed concern that the operators of the drone had not yet been apprehended - and could go on to cause more havoc.
All weary travellers could do was monitor the arrival and departure boards - showing many cancellations and delays to flights - and hope their Christmas getaways would not be ruined.
What has happened to passengers?
Travellers have found themselves unable to fly in and out of Gatwick.
Thousands were left stranded for hours inside the airport's terminal building, resorting to sleeping on floors and benches.
Some who spoke to the BBC included a couple hoping to honeymoon in New York and a seven-year-old who had been due to fly to Lapland. Others have found themselves stuck abroad.
Airport chief Mr Woodroofe refused to comment on the possibility of those affected by the chaos being awarded compensation.
The Civil Aviation Authority said it considered the event to be an "extraordinary circumstance", and therefore airlines were not obligated to pay any financial compensation to passengers.
But that does not mean passengers should be left out of pocket. It is the airline's responsibility to get anyone with a ticket to their destination, unless the passenger accepts a refund instead.
Alex Neill, from consumer rights group Which?, said people "may still be entitled to meals, refreshments, hotel accommodation or transfers".