Russia and Ukraine seem finally to have settled their row over gas supplies, raising hopes of an end to more than two weeks of shortages in Eastern and Central Europe.
What are the terms of the deal?
Ukraine will move from paying a subsidised rate for its gas to the market rate, in 2010. In 2009 it will pay the market rate less 20%.
Russia will pay a discounted rate to Ukraine for carrying its gas through pipelines to European customers in 2009, before paying the market rate from 2010.
"In the first quarter of 2009, the price of gas for Ukrainian customers will be $360 [£260] per 1,000 cubic metres. The price will change quarterly under the formula," said Russia's state energy firm Gazprom.
That compares to the market rate paid by European customers of about $450 - but is a major hike for Ukraine, which until December was paying only $179.50.
However, it is predicted that the $360 figure will fall dramatically. Gas prices tend to shadow oil prices, which have already plunged from record highs.
By midsummer, Ukraine could be paying as little as $150, Ronald Smith, a strategist at Moscow's Alfa Bank, told the Associated Press.
Ukrainian Prime Minister Yulia Tymoshenko said Kiev would end up paying less than $250, on average, over the course of 2009.
What sparked the crisis?
Russia cut gas supplies to Ukraine on New Year's Day, saying it would pump only enough for customers further down the pipeline.
Ukraine and Russia have faced negotiations over the renewal of gas supply contracts every year, but by midnight on 31 December 2008 they had failed to agree on the price Kiev should pay in 2009.
Gazprom asked for $418 per 1,000 cubic metres of gas, then $250.
But Ukraine rejected this, offering $235, prompting Gazprom to revert to its previous demand, of $418.
The two countries also failed to agree on a price Russia would pay Ukraine for gas transit to Europe.
Meanwhile, Gazprom demanded payment of about $2bn by the Ukrainian state energy firm Naftogaz: $1.6bn in backdated bills and a further in $450m fines for late payments.
Naftogaz says it has fulfilled its obligations by paying $1.5bn to cover its debts, but it disputes the fines.
Was that politics or economics?
Gazprom used to be a Russian ministry before becoming a private company, and it remains very closely connected to the state - Russian President Dmitry Medvedev is a former chairman of the company.
Critics say that Russia is using its energy resources as a political weapon to pressure European and former Soviet countries to adopt favourable stances towards Moscow.
But disrupted exports have damaged Russia's reputation as a reliable gas supplier.
Meanwhile, Gazprom has suggested that "political forces" in the pro-Western Ukrainian administration are seeking to provoke a wider confrontation with Russia.
Mr Putin has been highly critical of Ukraine's leaders, blaming the dispute on a "clan war" between Prime Minister Yulia Tymoshenko and President Viktor Yushchenko.
How was Europe's gas supply affected?
Gazprom controls about a third of the world's gas reserves and it is responsible for a quarter of Europe's supplies.
After a similar row in 2006, when Gazprom shut down its pipelines across Ukraine, Ukraine built up reserves to cover its needs for several months, and most other EU countries did the same.
This year, gas supplies were completely halted from 7 January, after Russia accused Ukraine of siphoning off gas meant for European customers, leaving more than a dozen countries without their expected supplies of Russian gas.
Some, like Bulgaria, Serbia and Bosnia, are almost completely dependent on supplies via Ukraine and so were left with major shortages, during a very cold spell in Europe.
The European Union called the supply cut "completely unacceptable", demanded immediate restoration and entered into shuttle diplomacy between Kiev and Moscow.
A deal reached on 12 January, whereby EU and Russian observers would monitor supplies across Ukraine, collapsed within hours. The EU said both sides had failed to meet its terms.
In the meantime European countries had to shut down industrial plants and domestic heating systems, find alternative sources of gas or switch energy plants to oil. Schools were shut and people had to revert to using log fires to heat their homes. Slovakia and Bulgaria mooted restarting mothballed nuclear reactors.
Is the EU happy about relying on Russian gas?
Gazprom had already embarked on plans for pipelines that bypass Ukraine and Belarus, former Soviet states which are currently essential for transit.
Gazprom has two major projects, Nord Stream and South Stream. Nord Stream will run for 1,200km along the bed of the Baltic Sea, and South Stream under the Black Sea. Gazprom has signed up big European partners: Italy's ENI for South Stream, and German companies E.ON Ruhrgas and Wintershall - along with Dutch provider Gasunie - for Nord Stream.
The EU has major concerns about security of supply and is moving ahead with a pipeline plan of its own. Nabucco will bring gas from Central Asia and the Caspian across Turkey into the European Union. But it will have only enough capacity to provide a small proportion, perhaps 5%, of Europe's needs.
So Europe needs Gazprom, and that is why European companies and their governments have actively embraced the two projects. Austria is likely to serve as a hub for both. EU officials say that even during the Cold War the Russian gas supply was stable, so it is better to rely on Gazprom than potentially unstable sources such as Turkmenistan and Uzbekistan.
Is the row now over?
Although the deal reached on 19 January 2009 is for a 10-year period, the bitter relationship between Russia and Ukraine means it would be unwise to predict an end to their gas rows.
Gazprom says the deal allows it to demand that Ukraine pay for gas in advance if it misses just one payment.
It also says Ukraine still owes it $600m in fines.
"There is no reason to believe that the situation with payments will improve [especially] after a significant price rise," Gazprom's chief Alexei Miller warned.