Europe's need for stable deliveries of Russian gas will loom large at an EU-Russia summit in the Swedish capital Stockholm on Wednesday.
The EU does not want another Russia-Ukraine gas crisis this winter
The August 2008 Russia-Georgia war and the disruption of Russian gas exports last winter led to frosty relations with the EU, and a new partnership deal is still being negotiated.
Russia's President Dmitry Medvedev will participate in the meeting, which is expected to include discussion of trade, climate change and human rights.
The EU has pushed for a mechanism to prevent any repeat of the January 2009 Russian gas shutdown, which left millions of people in Eastern Europe shivering in unheated homes and forced dozens of factories to suspend operations.
On Monday the EU and Russia agreed to set up an early warning system to ensure that EU importers of Russian gas would not be plunged into another crisis.
Russia's ambassador to the EU, Vladimir Chizhov, said it was more than a hotline - he described it as "a network of commitments" including "prompt information of any disruptions to our energy links".
The January crisis was triggered by a price dispute between Russia and Ukraine - and the EU remains wary of these two big neighbours' tense relations.
The EU Energy Commissioner, Andris Piebalgs, has ruled out granting a loan to Ukraine to help it pay off its debt to Russia. Russia's Prime Minister Vladimir Putin wanted the EU to grant such a loan - and he has warned that Russia will turn off the taps again if Ukraine fails to pay its bills.
Ukraine will hold presidential elections in January - and this is a foreign policy priority for the Kremlin, which dislikes President Viktor Yushchenko's Western-orientated stance. The election threatens to raise the stakes again in the politically charged energy sphere.
The EU is moving to diversify its energy supplies, all too aware of its reliance on Russia. But that does not stop multi-billion-dollar joint energy projects going ahead.
Russia has scored some significant diplomatic successes in recent months as it forges ahead with major new gas pipelines bypassing Ukraine.
Slovenia has given its approval for the Russian South Stream pipeline, which will transit several EU member states. It is seen as a rival to the EU's planned Nabucco pipeline, which will deliver Central Asian gas to Europe.
The Nord Stream pipeline, which will deliver Russian gas via the Baltic Sea to Germany, has been approved by Denmark, Finland and Sweden.
The EU wants clarity on Russia's long-running bid to join the World Trade Organization (WTO). The European Parliament is backing the bid, but says Russia must lower the transit fees it levies on goods transported by road and rail, as well as lift restrictions on meat and dairy produce.
The EU is concerned about Mr Putin's threat to widen Russia's WTO bid to include its neighbours Belarus and Kazakhstan, with whom it plans to form a customs union.
Sweden, currently holding the EU presidency, says the Russian plan complicates the bid and Sweden's EU Affairs Minister Cecilia Malmstroem warned that "major delays in the Russian accession will affect our bilateral relations".
Russia is the EU's third most important trading partner, after the US and China.
In the first half of 2009 Germany was by far the biggest EU exporter to Russia, accounting for 31% of the EU total (9.6bn euros; £8.5bn). Second was Italy (10%), then France (8%).
Germany was also the biggest EU importer from Russia (10.4bn euros or 20%), followed by the Netherlands (12%) and Italy (11%).
Machinery and vehicles accounted for more than 40% of EU exports to Russia in the same period. Energy accounted for nearly 75% of EU imports from Russia.
The Swedish EU presidency is keen to get firm pledges from European governments to take to the crunch Copenhagen climate summit in December, not least because the EU has assumed a leadership role on this issue.
So Sweden says one of the EU's top priorities on Wednesday "will be to urge Russia to present pledges on emissions reductions ahead of the UN Climate Change Conference in Copenhagen".
President Medvedev has set the goal of cutting Russia's CO2 emissions by 2020 by 10-15% compared with its emissions in 1990, when it was part of the Soviet Union. Plant closures have sharply reduced Russian emissions since Soviet times. But green activists want Russia to do much more.
Human rights abuses in Russia - especially in the North Caucasus - remain a big concern for the EU.
This year the European Parliament awarded its Sakharov Prize for Freedom of Thought to the Russian human rights group Memorial.
MEPs and EU ministers have condemned high-profile murders of human rights activists in Russia, demanding that the perpetrators be found and prosecuted.