• Russian and Ukrainian officials are conducting talks while the war continues to rage.
• Both sides have much to lose from the war that Russia began on Feb. 24.

As Russian forces pummel towns, villages and cities across Ukraine, pressure is growing on officials from both side to come to some sort of resolution, bringing an end to the destruction and bloodshed as soon as possible.

Previous attempts at talks appear to have made little progress, with the demands of both sides seemingly far apart, but there is room for compromise and signs that discussions are heading in the right direction.

In his nightly address on Monday, Ukraine's President Volodymyr Zelenskyy said talks that day had been "pretty good." Meanwhile, Russia said discussions over the weekend had made "substantial progress."

A fifth round of talks are set to take place on Tuesday with hopes that this impetus to reach a deal can continue.

Here is a brief guide to what each side wants:

What does Russia want?

One of the biggest questions posed by Russia's invasion of Ukraine, which began in earnest on Feb. 24., is what does President Vladimir Putin want — because it's not been made entirely clear.

Many close observers of the country have said that Putin's overarching aim is to restore Russia's sphere of influence over former Soviet territories like Ukraine, and to stop their slide towards the West.

In the near-term, Putin is seen wanting to topple Ukraine's pro-Western government and install a pro-Russian puppet leadership there in a bid to bring Ukraine back into Russia's orbit.

For its part, Russia has been clear in stating what it wants from talks with Ukraine:

It wants legal guarantees that Ukraine will never be allowed to NATO, the Western military alliance, and has since said that it wants Ukraine to sign a neutrality agreement and to change its constitution to cement this.

Moscow has demanded that Ukraine recognize the independence of two separatist, pro-Russian republics in eastern Ukraine, the so-called Peoples Republics of Donetsk and Lugansk. It has also demanded that Ukraine recognizes Crimea, which it annexed in 2014, as Russian territory. And it has called on Ukraine to cease all military activity.

Kremlin Spokesman Dmitry Peskov said last week that the war will stop "in a moment" if Ukraine agrees to these demands.

Russia has much to lose from the war with Ukraine, and has already been largely isolated on a geopolitical, financial and commercial stage, with businesses and brands pulling out of Russia in the wake of the war and the West's imposition of wide-ranging and hard-hitting sanctions on Russia, leaving its economy in tatters.

What does Ukraine want?

President Zelenskyy summed up Ukraine's aim when he said Monday that his country wants a "fair peace" with Russia. He has insisted the country is not willing to surrender, or accept ultimatums from Russia.

Ukraine has demanded a ceasefire with Russia, the withdrawal of Russian troops and has said it will not cede any of its territory to Russia. However, it's unclear whether this means it will refuse to recognize the breakaway pro-Russian republics in the Donbas or Crimea as Russian territory.

Ukraine has also signaled that it may compromise on future NATO membership, saying it would be willing to forego membership if it received "security guarantees" from the U.S. and NATO, ensuring its safety and security, in addition to any agreement with Russia.

An immediate priority for Ukraine has been the creation of humanitarian corridors to allow the safe evacuation of civilians, some of whom have been trying to survive under siege and unable to escape.

A key concern for Ukraine in recent weeks has been the southern port city of Mariupol. It is surrounded by Russian forces and has been facing near constant shelling while food, water and power in the city became scarce and previous attempts at a ceasefire failed.

There has been mixed success at creating humanitarian corridors in Ukraine, with some being created but directing Ukrainians into Russia, or its ally Belarus, while others have been scrapped amid reports of civilians coming under fire as they try to flee.

It is hoped that more civilians will be able to evacuate Mariupol on Tuesday, after a large number of civilians left on Monday.

Ukraine has said it plans to send a convoy with humanitarian supplies to the port city on Tuesday and hopes to take women and children out of the city on its way back, Reuters reported.

More than 2,500 residents have been killed in Mariupol since the Russian invasion on Feb. 24, according to a Ukrainian official on Monday cited by Reuters, although the figures are hard to verify. Russia has said that it does not target civilians despite evidence to the contrary with the targeting of hospitals and other public infrastructure.