European airports have reopened for business, almost a week after a cloud of ash from an Icelandic volcano paralysed the air travel industry.
About 75% of European flights are due to operate on Wednesday, according to air traffic agency Eurocontrol.
But delays are expected, as airlines try to cope with the backlog from the cancellation of 95,000 flights.
International air transport group IATA says the disruptions have cost the industry $1.7bn (£1.1bn).
Iceland's civil protection agency said the Eyjafjallajokull volcano had lost nearly 80% of its intensity since the weekend, although the situation remains changeable.
Airlines have now begun the enormous task of working through the backlog to get stranded passengers to their destinations.
Eurocontrol said it expected some 21,000 out of a normal weekday total of 28,000 flights to go ahead on Wednesday. It added that it was optimistic the situation would be back to normal in a few days' time.
Long queues of passengers formed at some of Europe's major airports, including in Paris, Frankfurt and Madrid.
Travel analysts said passengers with current tickets would be given priority, and those who were affected by cancellations would be put on waiting lists.
Weary passengers cheered and clapped as flights began to take off from airports.
Eve Dickinson, who was among the first to arrive back in Britain, said: "We're absolutely delighted to be home."
Britain reopened its airspace from 2200 local time (2100 GMT) on Tuesday, allowing long-haul flights to land at Heathrow airport, Europe's busiest.
A flight from Vancouver, Canada, was the first to arrive.
British Airways said it would operate all long-haul flights departing from Heathrow and Gatwick airports on Wednesday.
Air traffic controllers in Germany said all restrictions on the country's airspace had been lifted. Air France said its long-haul flights are now departing as normal, although services in parts of northern Europe remained suspended.
Around the world, airlines began putting on extra flights to clear the backlog of stranded travellers.
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Nats overreacted and closed airspace for no valid reason so I think it should pay
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Qantas, Singapore Airlines, Cathay Pacific and Virgin flights have begun taking off from Australia and New Zealand, while Air China and Japan Airlines announced that all their Europe flights would also be departing.
Coaches chartered by the British government have begun ferrying passengers arriving off long-haul flights at Madrid's airport to French ports for the crossing back to the UK.
In Calais there was a stand-off involving two coachloads of Britons who had travelled from Munich after arriving from various European destinations.
The passengers staged a sit-in saying they had been promised full passage to the UK. The stand-off was resolved after the British Foreign Office agreed to pay for the ferry crossing and their transfer by coach to their final destinations.
Business impact
European Transport Commissioner Siim Kallas has denied the EU took too long to respond to calls for airspace to be reopened, saying people's lives were at stake.
The UN's International Civil Aviation Organization (ICAO), meanwhile, said it would lead moves to develop a global standard for the concentration of ash in the air beyond which it was dangerous to fly.
But final decisions about safety would remain up to governments, ICAO Council president Roberto Kobeh Gonzalez said.
The flight ban was imposed because in the high temperatures of an engine turbine, ash can turn to molten glass and cripple the engine.
As travellers scrambled for other modes of transport, ferry and railway companies enjoyed an unexpected bonanza, while some car-hire firms were reportedly increasing charges.
But many other businesses have been hit hard by the chaos.
The carmaker BMW said it was suspending production at three of its plants in Germany because of interruptions in the supply of parts. In Japan, Nissan also suspended production lines, while Honda announced a partial halt to production.
Blocked shipments of goods are also reportedly stacking up in Asian countries including China, South Korea and Bangladesh, while some African exporters of fresh flowers and vegetables are having to throw away tonnes of rotting stock.
For all the chaos that the Eyjafjallajokull volcano has already created, scientists say the ash cloud may only be the start. There are concerns the eruption could set off the nearby, larger Katla volcano, which sits on the Myrdalsjokull glacier, but officials said no activity had been detected. Its last major eruption was in 1918.