But for all the anxiety about Ukraine's future — bolstered by Vladimir Putin's contention the country is on the verge of civil war — the top diplomats of Ukraine, Russia, the United States and the European Union may find their positions so far apart that no one can find a compromise.
A look at the parties in the talks and their levers of power:
What Russia says it wants: Since the ouster of Ukraine's Russia-friendly President Viktor Yanukovych in February, Moscow has consistently pushed for Ukraine to become a federalized state, in which the country's regions would have more powers outside the central government in Kyiv. That could let some Ukraine regions pursue closer trade ties with Russia — or even vote to join Russia.
What it really wants: It deeply wants Ukraine to stay away from NATO membership and to be drawn back into Russia's orbit instead of coming under the sway of the European Union.
What it would settle for: Ukraine not in NATO or the EU and in a trade confederation that Moscow will build, according to Fyodor Lukyanov, editor of the Russia In Global Affairs journal. Russia is likely to push hard for these, even at the risk of more sanctions. "If further sanctions are imposed, this is the price Putin will accept and certainly he will not concede," said analyst Masha Lipman of the Carnegie Moscow Center.
What the U.S. says it wants: The Obama administration wants Russia to drop its claim to have annexed Crimea and drawn down its troops on the strategic peninsula to pre-crisis levels. The White House is also demanding the Kremlin halt provocative actions by pro-Russian militia in eastern Ukraine that the West believes are being funded and co-ordinated by Moscow.
What it really wants: The U.S. wants the above — but it also wants Russia to stop bullying Ukraine, especially in the energy sector, which it sees as a worrisome precedent for other former Soviet republics such as Georgia, Moldova and the Baltics. Washington also still needs Russian co-operation on thorny diplomatic issues such as Iran.
What it would settle for: The U.S. will not recognize Russia's annexation of Crimea but that's by and large a done deal. The U.S. would settle for the Kremlin to just halt its provocations in eastern and southern Ukraine and end any efforts at destabilizing the country.
What Ukraine says it wants: Prime Minister Arseniy Yatsenyuk says for the Geneva talks "there is only one, fundamental directive: Russia must pull out its saboteur groups and denounce terrorists."
What it really wants: Analyst Vadim Karasyov says behind the scenes, Ukraine will be talking about how best to decentralize power so regions don't want to break away and join Russia. "They will be searching for some kind of compromise with Russia because nobody wants to go to war," he said.
What it would settle for: Ukraine wants Russia to stop supporting insurgents in the east. It is also likely to be playing for time, hoping to keep the situation on the ground comparatively calm ahead of the May 25 presidential election. If that vote goes smoothly, Russia will lose its leverage of tarring Ukraine as being led by an illegitimate government.
THE EUROPEAN UNION
What the EU says it wants: EU foreign policy chief Catherine Ashton's spokeswoman says the 28-nation bloc wants direct talks between Russia and Ukraine to calm down the tensions in eastern Ukraine. If that situation deteriorates further, EU leaders have threatened to introduce biting economic sanctions against Russia.
What it really wants: The EU wants pro-Russian groups to stop seizing government facilities in eastern Ukraine. It also wants to lessen Ukraine's economic dependency on Russia, offering a wide-ranging aid package, a free trade agreement and help in reducing the country's reliance on Russian natural gas.
What it would settle for: Tacitly, though not legally, the EU has accepted Ukraine's loss of the Crimean Peninsula to Russia but it won't accept a further partition of the country. It has hinted it could accommodate some of Russia's concerns about the EU-Ukraine free trade agreement if this could smooth Kyiv's dealings with Moscow.
Maria Danilova in Kyiv, Ukraine, and Juergen Baetz in Brussels contributed to this report.