But the gridlock created by Iceland's volcanic ash plume was far from over: Officials said it would be weeks before all stranded travelers could be brought home.
In another positive development, Germany's air traffic controllers said Wednesday they had lifted all restrictions for the country's airspace.
Airlines were already being permitted to operate a limited number of flights to and from all airports - up to 800 flights in total Tuesday - under so-called visual flight rules.
On the business front, the International Air Transport Association says disruptions to European air travel from the volcanic ash cloud have cost the industry at least $1.7 billion.
Passengers wept with relief as flights took off from Paris' Charles de Gaulle Airport, Amsterdam and elsewhere. A jetliner from Vancouver, British Columbia, was the first to land at London's Heathrow airport, the continent's busiest, since the volcano erupted last week.
The first passenger to emerge from Heathrow was Neil Rodgers, a finance director from England who had been stranded in Vancouver, Canada, for five days, CBS News reports. Rodgers told CBS News that his flight, British Airways 084, was held in a holding pattern over the U.K. while the pilots were directed where to land.
Travelers cheered as the first European flights took off.
Chris James, arriving at Heathrow from Mauritius, told the British Broadcasting Corp. that passengers on his flight didn't know they would land in London until 45 minutes before their plane touched down.
"Initially it was quite a stressful situation, we didn't know what was happening," James said.
Aviation expert Michael Boyd told CBS' "The Early Show" it could take up to seven days for airlines to return to normal schedules, adding that those people stranded in airports could expect to reach their destinations in the next four days.
The Eurocontrol air traffic agency said it expected just under half of the 27,500 flights over Europe to go ahead Tuesday, a marked improvement over the last few days. The agency predicted close to normal takeoffs by Friday.
It was the first day since the April 14 eruption of Iceland's Eyjafjallajokull volcano - dormant for nearly 200 years - that travelers were given a reason for hope.
"The situation today is much improved," said Brian Flynn, deputy head of operations at the Brussels-based agency.
But with more than 95,000 flights canceled in the last week alone, airlines faced the enormous task of working through the backlog to get passengers where they want to go - a challenge that could take days or even weeks.
CBS News Correspondent Richard Roth reports flying after the ash cloud will be like recovering from the disruption to travel after 9/11, according to the airline industry, except this has been twice as long and worse.
Global airline schedules depend on the synchronized movement of interlocking parts, Roth reports. The shutdown left planes and flight crews out of position. Travelers may be waiting, but the whole puzzle needs reassembling.
"It's pretty bad," said CBS Travel Editor Peter Greenberg. "They're herding cats right now. The problem is they've got to put planes back in places they need to be; they have to put flight crews together with planes, and they're not together. They're out of sequence and out of cycle. This could take at least 96 hours just to get the planes where they need to be."
Passengers with current tickets were being given priority; those who had been stranded for days were told to either buy a new ticket or take their chances using the old one - a wait that could be days or weeks for the next available seat.
"Once your flight's canceled, you go to the back of the queue," said Laurie Price, director of aviation strategy at consultant Mott Macdonald, who was stranded in Halifax, Canada. "It seems intrinsically unfair."
The volcano that prompted the turmoil continued to rumble, and tremors could be heard and felt as far as 15 miles from the crater.
"It's like a shaking in the belly. People in the area are disturbed by this," said Kristin Vogfjord, a geologist at the Icelandic Met Office.
Land and water at farms in the ash zone have suffered since the volcano's eruption, with normally green pastures turned black and hard by the ash.
Vigtus Andresson said grazing land and water on his farm near the town of Hvolsvollur were contaminated, making it necessary to evacuate many of the horses and sheep he raises there. He said he also must slaughter some of his 29 horses because there is no place for them to go.
Scientists were worried that the eruption could trigger an even larger eruption at the nearby Katla volcano, which sits on the massive Myrdalsjokull icecap. Its last major eruption was in 1918.
"The activity of one volcano sometimes triggers the next one, and Katla has been active together with Eyjafjallajokull in the past," said Pall Einarsson, professor of geophysics at the Institute of Earth Sciences at the University of Iceland.
Volcano experts say that should such an eruption occur, air travelers might expect more disruptions, depending on prevailing winds. Of Iceland's eight volcanic eruptions in the last 40 years, only the recent one at Eyjafjallajokull was followed by winds blowing southeast toward northern Europe.
While seismic activity at the volcano had increased, the ash plume appeared to be shrinking - though it wasn't moving very fast.
Sarah Holland of Britain's Meteorological office said the plume was being held over Britain by a high pressure system that showed no signs of changing.
"The weather patterns are very static at the moment. It's unusual to have that for such a long period of time," she said. "Unfortunately, it looks like it's going to stay that way for the next couple of days, bringing the ash over the U.K."
Early on Tuesday, a Eurocontrol volcanic ash map listed the airspace between Iceland and Britain and Ireland as a no-fly zone, along with much of the Baltic Sea and surrounding area.
Still, planes were allowed to fly above 20,000 feet in Britain, ahead of the reopening of airspace nationwide Tuesday evening.
Dozens of flights departed and arrived at Amsterdam's Schiphol Airport as the government announced that flights could be carried out in darkness using instruments. Airports in Switzerland, central Europe and Scandinavia also reopened, and some flights took off from Asia headed for southern Europe, where air travel was not affected. Spain piled on extra buses, trains and ferries to handle an expected rush of passengers.
Polish aviation authorities said they planned to reopen the country's airspace Wednesday morning.
Even the U.S. Air Force was grounded. Capt. Alysia Harvey, the spokeswoman for the U.S. Air Force's 48th Fighter Wing at Lakenheath, said all sorties had been canceled there since last Thursday. Lakenheath is the largest U.S. air base in England, and the only one in Europe that has an F-15 fighter wing.
"Flying was canceled because it's difficult to predict exactly where the cloud is going to be or the effect it will have on aircraft engines," she said.
Meanwhile, tens of thousands of Britons sought a way home.
Britain's Foreign Office acknowledged the enormity of the problem, informing Britons abroad that it may take a "matter of weeks before everyone can be repatriated."
Tom and Natalie Smith and their children Ben and Joanne, from Bristol, England, found themselves stranded after spending a week on the Costa Brava in Spain.
"We should have returned to work this morning," Tom Smith said. "Natalie is a diabetic and so that is also a concern as she may run out of medication depending on how long it takes to get back."
The government advised Britons to remain in close contact with their airline. Those in Europe were told to make their way to the French port of Calais, other Channel ports or a northern European port.
Thousands converged on the coast from across Europe by car, train and bus, evoking memories for some of the evacuation of the British army from Nazi-occupied France through the port of Dunkirk in 1940.
"You could say it is a bit of Dunkirk spirit," said Stanley Johnson, father of London mayor Boris Johnson, who was among some 800 soldiers and civilians picked up in Spain by a Royal Navy warship, HMS Albion.
The aviation industry - facing losses of more than $1 billion - has sharply criticized European governments' handling of the disruption that grounded thousands of flights on the continent.
"I don't believe it was necessary to impose a blanket ban on all U.K. airspace last Thursday," said Willie Walsh, chief executive of British Airways, which has canceled about 500 flights a day in the past five days. "My personal belief is that we could have safely continued operating for a period of time."
Some carriers were using bigger planes and more flights, while others were hiring buses to help get customers to their destinations.
The U.N.'s International Civil Aviation Organization said Tuesday it will start work on setting global standards for the concentration of ashes that could affect airplane engines.
Raymond Benjamin, secretary-general of the U.N. agency responsible for aviation safety, said ICAO convened a special meeting of its governing council on Monday on ash standards following the global disruption to air travel caused by the volcanic eruption.
He said the council decided to convene a group including representatives from industry, manufacturers, governments, scientists, and the International Air Transport Association "to start working on these standards." Benjamin spoke to reporters after meeting U.N. Secretary-General Ban Ki-moon.