Cypriot President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci, who have negotiated for more than 18 months in the run-up to the talks, have been among the most outspoken proponents of a deal.
But both acknowledge key issues still need to be thrashed out, with the prospects of solving one of the world's longest-running geopolitical disputes remaining murky.
The United Nations has pulled out all the stops in its bid for a deal, eyeing the best chance of a settlement in more than a decade.
“It is a real possibility that 2017 will be the year when the Cypriots, themselves, freely decide to turn the page of history,” said UN envoy Espen Barth Eide, who will receive the two leaders from around 8.45 am (0745 GMT).
On the eve of the talks, Greek and Turkish residents gathered in Nicosia to hear musicians from both sides perform at a “Countdown to Peace” concert, with the setlist including The Beatles' “Come Together”.
“We are ready. So we send a message to our leaders, to the whole world, that we, the people of this island, we can live together,” said Marilena Evangelou, chief editor of the online edition of Politis, one of several media outlets that organised the concert.
But some experts believe the Geneva talks are a disaster waiting to happen because of deep divisions on core issues such as property, territorial adjustments and security.
'Tough week' ahead
Leaving for Geneva on Sunday, Akinci described the talks as a “crossroads”.
“We are not at a point where Geneva will mark the final conclusion. We need to be cautious,” he said.
“We are expecting a tough week.”
And Anastasiades tweeted that he was heading to the talks “with hope, confidence and unity” after earlier striking a note of caution, warning of “significant differences on substantive issues fundamental to a Cyprus solution”.
Cyprus, home to around one million people, has been divided since 1974, when Turkish troops invaded the island in response to an Athens-inspired coup seeking union with Greece.
Nine years later, Turkish Cypriot leaders declared a breakaway state in the north which is recognised only by Ankara.
The years of communal violence, which culminated in the Turkish invasion, saw tens of thousands from both sides flee their homes — and they remain displaced to this day.
It has always been agreed that some of the territory currently controlled by the Turkish Cypriots will be ceded to Greek Cypriot control in any peace deal.
Just how much and which land they should give up has hampered four decades of talks.
The issue is vital because the two leaders have pledged to put any deal to the vote in their respective communities.
In 2004, a majority of Turkish Cypriots backed a UN reunification plan but it was overwhelmingly rejected by Greek Cypriots.
The sides also remain far apart on how many Greek Cypriots should be able to return to homes they fled in 1974, with Akinci determined to minimise the number of Turkish Cypriots who would be displaced for a second time.
And there are differences over security arrangements with Anastasiades wanting Turkish troops to leave the island but Akinci determined to keep a military presence.
Akinci also insists on a rotating presidency with a Turkish Cypriot elected every two years — a proposal unpopular among Greek Cypriots.
The two sides will on Wednesday provide maps of their proposals for the internal boundaries of a future bi-zonal federation.
If that goes to plan, they will be joined from Thursday by the leaders of the island's three guarantor powers — former colonial ruler Britain, Greece and Turkey.
Hubert Faustmann, a history and political science professor at the University of Nicosia, said he believed the talks would be a stepping stone.
“I expect neither a success nor a failure but the beginning of a series of final round talks under the participation of the guarantor powers with 'observers' invited from the EU and Security Council,” he told AFP.