Who is winning the war in Ukraine?

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Russian forces are advancing in eastern Ukraine faster than they have done in a long time, Vladimir Putin has claimed, raising fears that Ukraine's overstretched defences could be overrun.

Speaking to secondary school pupils on Monday, the Russian president said troops were advancing several kilometres per day as Moscow attempts to smash through Ukraine's defensive line in the Donbas.

Despite a major Ukrainian incursion into Russia's Kursk region that began a month ago, the numerically stronger Russian army has in recent weeks been "thrusting relatively swiftly through settlements in eastern Ukraine on the approach to the strategically important city of Pokrovsk", Reuters reported.

What about Ukraine's incursion into Russia?

Kyiv's surprise incursion into Russia's southern Kursk region was "designed partly to pressure Russian generals to scramble forces from other parts of the eastern front in Ukraine", said Reuters. They have, so far, failed to take the bait despite the continued presence of Ukrainian forces on Russian soil causing considerable embarrassment to the Kremlin and anger among the local population.

The commander-in-chief of the Ukrainian Armed Forces, Oleksandr Syrsky, admitted that Russia has instead intensified its efforts and deployed its most combat-ready units to the Pokrovsk front in Donetsk.

By redirecting resources away from defensive efforts in the eastern Donetsk region, Ukraine is "betting that other parts of the 750-mile front won't collapse, that it will not lose a large number of soldiers and equipment in Kursk, and that the benefits from its operations in Kursk will outweigh the costs sustained elsewhere", said Foreign Affairs.

Yet it "remains unclear how Ukraine's leaders intend to translate this tactical success into strategic or political gains" with the incursion offering "opportunities," but also carrying "considerable risks and costs".

How many Russian and Ukrainian troops have died in the conflict?

True casualty figures are "notoriously difficult to pin down", said Newsweek, and "experts caution that both sides likely inflate the other's reported losses".

In May, an investigation by the BBC's Russian unit was able to identify 52,155 named Russian military personnel who have died in the conflict so far, but used statistical data on excess deaths to suggest that the true figure could be more than 100,000. The BBC reported that the UK Ministry of Defence estimated there were 70,000 Russian casualties in Ukraine in May and June alone.

As for Ukraine, it is "extremely unusual" for the country's media to report on casualty figures, reported The Times. Volodymyr Zelenskyy said in February that 31,000 Ukrainian soldiers had died since Russia invaded in February 2022, but US officials claimed last August that the Ukrainian death toll was more than twice that figure.

What does victory look like for each side?

Before Russia launched its invasion in February 2022, Putin outlined the objectives of what he called a "special military operation". His goal, he claimed, was to "denazify" and "demilitarise" Ukraine, and to defend Donetsk and Luhansk, the two eastern Ukrainian territories occupied by Russian proxy forces since 2014.

Another objective, although never explicitly stated, was to topple the Ukrainian government and remove the country's president, Zelenskyy. "The enemy has designated me as target number one; my family is target number two," said Zelenskyy shortly after the invasion. Russian troops made two attempts to storm the presidential compound.

Russia shifted its objectives, however, about a month into the invasion, after Russian forces were forced to retreat from Kyiv and Chernihiv. According to the Kremlin, its main goal became the "liberation of the Donbas", including the regions of Kherson and Zaporizhzhia – but Moscow has made little progress in achieving this aim.

Ukraine's main objective is the liberation of its occupied territories. That includes not just those held by Russia since the February 2022 invasion, but a return to its internationally recognised borders, including Crimea.

Can Ukraine win the war?

As Ukraine battles to slow the advance of Russia further into its territory the outcome of the war looks increasingly likely to be decided by two key factors: supply of soldiers and maintaining international support.

Earlier this year, Zelenskyy lowered the age of military conscription in Ukraine to 25 in an attempt to boost troop numbers. But conscription remains a touchy topic in Ukraine, and officials have had to tread lightly amid dwindling enthusiasm for military service. "We don't only have a military crisis – we have a political one," one of the officers speaking to Politico warned.

Ukraine's "inherent weakness is that it depends on others for funding and arms", wrote the BBC's international editor, Jeremy Bowen, while Russia – in addition to an advantage in raw manpower – "makes most of its own weapons" and is "buying drones from Iran and ammunition from North Korea" with no limitations on how they are used.

For now, Russia retains an "advantage in manpower, equipment and ammunition", said Foreign Affairs. This advantage has "not proved decisive, or led to operationally significant breakthroughs", but Russian forces have steadily gained 750 square miles of territory since October 2023, and with the pace of that advance now accelerating, Ukraine's position looks "increasingly precarious along parts of the front".

This "mismatch" between Moscow and Kyiv remains a "key thread" of Zelenskyy's ongoing call for more Western help, said the BBC's Europe correspondent, Nick Beake.

Ukraine's president has argued that much greater American and European assistance in air defence is more vital than ever and that permission to use foreign-made long range missiles to strike further into Russia urgently needs to be granted, "especially now that Kyiv is fighting a battle at home and abroad".

If the "worst-case scenario" for Ukraine was to materialise, said CNN, namely if the US stopped providing aid, Europe did not step up its assistance and Ukraine was not able to access the $50 billion or so in frozen Russian assets promised to it by the G7, then Russia would "likely start to make much bigger gains" which could force Kyiv to the negotiating table.