Flights are now departing and arriving at UK airports after the Civil Aviation Authority (CAA) relaxed its rules, but airlines warn of continued delays and cancellations.
The CAA changed its rules on flying through ash late last night. A spokesperson said: "The major barrier to resuming flight has been understanding tolerance levels of aircraft to ash. Manufacturers have now agreed increased tolerance levels in low ash density areas."
The CAA said it had taken the decision after "thorough gathering of data and analysis by experts". An area in the north of Scotland remains out of bounds, as the ash density is considered too high.
Airlines are now attempting to repatriate travellers stuck abroad, and are warning passengers to expect further delays.
Easyjet said: "Due to the extent of the disruption, it will take several days to resume normal operations and delays are likely."
Easyjet has started flights again today, but is not allowing online check-in. The airline said: "All passengers must go to the airport check-in desks on arrival at the airport, even if you have already checked in online. This will allow us to transfer as many disrupted passengers as possible on to available seats."
British Airways has cancelled some shorthaul flights before 1pm today, but plans to operate all its longhaul flights from London Heathrow and Gatwick.
Flybe has cancelled all its flights before 1pm, but plans to operate as many services as it can after that time, although some remain cancelled. Some flights previously due to depart before 1pm have been rescheduled for later this afternoon.
Virgin Atlantic said it plans to operate some flights today, but hopes to resume its full schedule as soon as possible. The airline warned: "We strongly urge passengers not to travel to the airport over the next few days unless they have a confirmed booking on a flight which is confirmed to operate."
Aer Arann will resume flights from 1pm today.
Ryanair will operate its flights as scheduled from 5am tomorrow morning, between the UK and continental Europe. Flights between the UK and Ireland will start from 5am on Friday morning.
Aer Lingus has cancelled all its UK and European flights scheduled to depart before 1pm, but it plans to operate the majority of its transatlantic flights today and all scheduled flights after 1pm.
The Board of Airline Representatives in the UK (BAR UK), representing more than 90 airlines, welcomed the decision to re-open UK airspace
Mike Carrivick, CEO of BAR UK, said: "Safety is understandably the number one priority for everyone and our member airlines recognise the cooperation that took place between NATS, CAA and the Department for Transport (DfT) that enabled the re-opening of UK airspace.
"A number of airlines have been proactively supporting the required research providing test flight data in order to get their customers flying again. Whilst a review of the length of closure endured is certain to take place and important lessons will surely be learned, our priority must be to ensure a rapid return to full service levels as soon as possible."