Here are three scenarios of what could happen over the coming weeks and months, and the economic impacts.
CLOUD CLEARS SWIFTLY
The volcano could cease erupting; simply stop emitting ash; winds could shift away from Europe; or the gas cloud could be dispersed unexpectedly quickly. So far, none of these shows any signs of happening.
Airlines and air freight companies would immediately scramble to make up for lost time, repatriate and relocate passengers, aircraft and cargo.
• Airlines would still have lost some 130 million a day during the shutdown, and airline stocks would probably still fall today as markets take into account losses over the weekend.
• Even if the cloud clears, some travel will still be cancelled in the coming days. Some firms are asking employees to cancel non-essential European flights over the next 7-10 days.
Howard Archer, chief economist at IHS Global Insight, said: "The overall economic impact should be limited even if the problem persists for several more days."
CLOUD CLEARS, ERUPTION CONTINUES
Experts warn that as long as the eruption continues, the risk remains that a renewed outflow of ash or certain wind patterns could produce the same effect again.
The threat of a renewed shut-down might deter both business and leisure travellers from booking flights, holidays and hotels.
• Airline industry stocks could underperform as markets factor in a risk premium. Rail, road, sea cargo and teleconference firms could see an increase in demand.
• Firms might take on additional stocks to reduce their reliance on "just-in-time" resupply by air cargo.
• Any return of the cloud would again hit airline and travel stocks as well as potentially undermining regional growth.
• Much would depend on whether the current eruption triggers Iceland's nearby and much larger Katla volcano, further increasing the potential impact.
Chris Weafer, chief strategist at Russian bank Uralsib, said: "The volcano has the potential to undermine Europe's fragile recovery and that would have global consequences.
"So much global trade and commerce is airborne these days that any extended disruption will have immediate impact on investment and growth."
CLOUD REMAINS, EUROPE REMAINS SHUT DOWN
If the cloud remains stubbornly over Europe for weeks or months, the travel sector would take a serious hit. Wider industries would also be affected, from high-tech manufacturing to supermarkets and event organisers.
• This would be devastating news for the airline sector, possibly driving some of the weakest operators to the wall.
• Overall European growth might be affected, slowing the recovery from recession. Europe might lag further behind the rest of the world in the global recovery.
• Teleconference, shipping, rail and road transport operators would benefit. So would airports just outside the cloud, suddenly in great demand from airlines and shipping firms as new hubs. That could benefit countries along the edge of the cloud including Ukraine, Turkey, as well as Portugal, Italy, Greece and Spain.
• Western military resupply flights to Afghanistan would be heavily affected. Western European troop contributors would become entirely dependent on the United States for supplies and medical evacuation flights.
• Major international meetings may have to be cancelled, rescheduled or simply go ahead without senior European policymakers.
Vanessa Rossi, senior economic fellow at the think-tank Chatham House, said that losses in tourism and travel could knock 1 to 2 percentage points off regional growth in Europe.
"That would mean a lot of European countries wouldn't get any growth this year," she said. "It would literally stifle the recovery."