Members of Donald Trump's negotiating team have been in Kyiv, Geneva, Miami and Abu Dhabi recently, trying to secure a peace deal between Ukraine and its Russian invaders.
Those efforts are expected to continue this week as Trump's special envoy Steven Witkoff heads to Moscow to talk some more.
An American proposal kicked off the fresh round of negotiations more than a week ago, but it was quickly slammed by critics as favouring Russia.
Ukraine and Europe were reportedly shocked by some of its contents, in particular those that appeared to hand Russian president Vladimir Putin much of what he wanted.
The so-called 28-point peace plan — which Trump has since referred to as a "concept" — was the subject of messy leaks to US media and accusations it was too sympathetic to Moscow.
All of which amped up the drama around the proposal that appeared to contain enough of that on its own.
Since then, the peace plan has been redrafted and "refined", according to Trump and Ukrainian president Volodymyr Zelenskyy. It is now reportedly a proposal of fewer points with plenty of negotiation left to happen.
Russia, most notably, is yet to respond, but the Associated Press is reporting the Kremlin has seen a copy of a revised version via backchannels.
Kyiv and Moscow are reportedly stuck on the same issues that have plagued peace talks in the past: the division of territory, in particular the land Russia wants but its military hasn't been able to gain, as well as how security will be guaranteed in Ukraine in the future.
Russia wants no NATO troops on the ground, but the US has previously floated offering a NATO-style guarantee, where any future attack on Ukraine would be considered an attack on America too.
Donald Trump's administration has previously said ending Russia's war would likely require Ukraine to make territory concessions, but Zelenskyy has repeatedly said he cannot cede land to his country's invaders.
Analysts from the Institute for the Study of War (ISW) say Russia's rate of advance across the entire war theatre has increased since Putin stepped foot on US soil in August for the Alaska summit, but a military victory for the Russian leader is still "far from certain".
Looking at the map, there are five regions at the heart of any genuine negotiations: Luhansk, Donetsk, Kherson, Zaporizhzhia and Crimea.
Putin wants them all.
Two regions in eastern Ukraine that border Russia are collectively known as the Donbas – Luhansk and Donetsk.
Vladimir Putin has long coveted these regions and sees them as central to his war effort.
Luhansk is now occupied by Putin's forces, according to ISW Critical Threats data and under the original 28-point US proposal, it would be recognised as "de facto" Russia.
There are some areas where Putin's forces have moved west of the Luhansk border and into Ukrainian territory bordering Russia.
It's unclear what is currently being proposed for this territory, but the original 28-point plan suggested Russia would be asked to "give up other agreed-upon territories" they control outside of the five eastern regions.
Further south, Putin's army controls a large part of Donetsk, but importantly, it has not been able to capture the entire region, as ISW data shows.
In 2014, when Russia illegally annexed Crimea, it also backed separatists in Luhansk and Donetsk to break away from Ukraine.
On February 21, 2022, Putin signed a presidential decree recognising the independence of the two regions, and a day later his tanks rolled towards Kyiv.
He never took the capital, but he is determined to take Donetsk and while his military grinds forward in the region, its advance has slowed.
Analysis from the ISW says taking the entire region would likely be a "years-long battle" and that the current rate of advance does not indicate Putin's military is on the verge of a victory there.
Before Europe responded, the US proposal said Ukraine would withdraw from the part of Donetsk it still controls and that area would become a "neutral demilitarised buffer zone, internationally recognised as territory belonging to Russia".
Zelenskyy and European leaders voiced opposition to Russia controlling an area it has not been able to gain militarily. And in one version of a draft counterproposal published by Reuters, European leaders said territory negotiations should begin from the current front line.
Reuters has reported the idea of a DMZ in Donetsk has been put on hold for now.
As Ukraine knows and fears, if what's left of Donetsk was controlled by Russia, its enemy would be in a far more favourable position were it to ignore any eventual ceasefire promise and attack again, as ISW analysts have repeatedly pointed out.
And any proposal that swept Ukrainian-controlled Donetsk areas into a DMZ, or brought them under Russian recognition, would impact hundreds of thousands of people.
The new front line would sit closer to Kyiv and would be beyond the Ukrainian fortifications that did their job and prevented Russia from consuming the region at the pace its leader would have preferred.
Ukraine has worked for years to fortify areas of Donetsk, with the so-called "fortress belt" of cities running through it — Slovyansk, Kramatorsk and Kostyantynivka.
Capturing the town of Pokrovsk has been a priority for Russian forces and as of last week, they had consolidated advances in 66 per cent of the city, according to ISW analysis.
However, Ukraine's defence has slowed their rate of advance there and after more than 100 days of operating in the town, Russia had not been able to seize it.
Russian advances in Donetsk may be considered slow, but further south, there have been rapid gains.
In recent weeks, Russia's swift advances have been in the east of the Dnipropetrovsk region as well as in the region of Zaporizhzhia.
The current front line also divides the region of Zaporizhzhia in two. Under the original US proposal, that would have been how the recognition of Zaporizhzhia was carved up.
Again, the European counterproposal noted territory discussions should begin at the current front line.
Within this region is the Zaporizhzhia power plant — an asset currently controlled by Russia. The International Atomic Energy Agency boss has asked that this site be put under a cooperation agreement, no matter who controls it in a peace deal.
The two remaining regions on Putin's wish list are Crimea and Kherson.
The Crimean peninsula was illegally annexed by Russia in 2014 and under draft US proposal, it would be recognised as de facto Russian.
At the south-east of Ukraine, is Kherson, a region now largely controlled by Russia, so any carving up of territory along the front line would see most of it go to Putin.
Putin's problem with de facto
It was in October 2022 that Putin signed treaties that purported to absorb Donetsk, Luhansk, Zaporizhzhia and Kherson into Russia.
The illegal annexation followed Kremlin-orchestrated "referendums" that Kyiv and the West dismissed as illegitimate.
Some reporting out of the Alaska summit said Putin was willing to divide Zaporizhzhia and Kherson along the front line in exchange for the Donbas.
But previously he has called the full withdrawal of Ukrainian troops from Donetsk, Luhansk, Kherson and Zaporizhzhia as "very simple" conditions for peace.
In Putin's eyes, these regions are Russian.
And when he was speaking to the press just last week about the Donbas, he talked about Ukrainian forces leaving "the territories they occupy".
"Then the hostilities will cease," he said.
In previous comments, Zelenskyy has said some areas under Russian control might be recognised as temporarily de facto occupied, but he has ruled out any de jure, or lawful, recognition.
Ukrainian representatives have repeatedly made the point their nation's constitution prohibits such a move.
At the recent and unusually candid press conference, Putin said the mention of "de facto" recognition for Crimea and the Donbas in the US proposal was "one of the issues that should be addressed in our negotiations with the American side".
He called the issue of recognition "one of the key points".
In a recent article in The Atlantic, Ukraine's then-chief negotiator Andri Yermak appeared to make one thing very clear, saying: "As long as Zelenskyy is president, no-one should count on us giving up territory."
"All we can realistically talk about right now is really to define the line of contact. And that's what we need to do."
After nearly four years of war, Russian forces control about 19 per cent of Ukraine and a senior Russian diplomat recently reiterated that Russia had no plans to make big concessions on its ambitions.
Other terms that have become sticking points as proposals are drafted and redrafted include the question of NATO membership for Ukraine and possible limits on the size of its military.
Under the original US proposal, the Ukrainian military would be capped at 600,000 — fewer soldiers than it currently employs to defend itself against Russia, according to Zelenskyy.
There are red lines that Putin will not cross, perhaps the most notable is his long-sought-after conquest of the Donbas.
"If they do not leave, we will achieve it militarily," he said.
