Georgia is voting in presidential elections that will bring to an end a decade in power for pro-Western President Mikheil Saakashvili.
The frontrunner among the 23 candidates is a close ally of Prime Minister Bidzina Ivanishvili, Mr Saakashvili's bitter rival.
Following the polls, constitutional amendments will significantly reduce presidential powers.
Mr Saakashvili is barred from standing as he has already served two terms.
Mr Ivanishvili's win in parliamentary elections last year ushered in the former Soviet republic's first legal transfer of power.
The billionaire businessman also intends to resign within weeks of the vote, saying he has achieved his aims.
He has called Sunday's vote Georgia's "first European-style election".
Polling stations are open from 08:00 local time (04:00 GMT) until 20:00. Final results must be published no later than 16 November.
If no candidate wins more than 50% of the vote, a run-off between the two top-placed candidates must be held two weeks after the results of the first round are published.
Opinion polls suggest a win for philosopher and former Education Minister Giorgi Margvelashvili, a member of Mr Ivanishvili's Georgian Dream coalition.
But a second round with David Bakratze, who represents Mr Saakashvili's United National Movement (UNM) remains a possibility.
Nino Burjenadze, another top contender, is one the most well known female politicians in Georgia.
"It is the first time that the candidate from the ruling party is not using administrative resources to boost his campaign," Mr Ivanishvili told the BBC.
"The election is taking place is a peaceful and balanced environment. This is the first European-style election in Georgian history."
Unlike most elections in other post-Soviet countries, this vote in Georgia is a genuine process with vibrant campaigns and a wide choice of candidates, says the BBC's Rayhan Demytrie in the capital Tbilisi.
The country is moving closer to a parliamentary democracy although the president will formally remain the head of state and retain an important role in foreign policy, our correspondent adds.
Since coming to power in the bloodless 2003 "Rose Revolution" Mr Saakashvili has implemented reforms which helped root out corruption.
He pursued a pro-Western foreign policy and improved public services in the Caucasus republic, where poverty remains widespread.
But the country's prime minister, who is also Georgia's richest man, has dismissed these achievements, calling Mr Saakashvili a "liar" and a "dictator".
He has indicated that the outgoing president could face questioning or even prosecution over the alleged crimes of his government after his term ends.
Mr Ivanishvili has not yet named a successor as prime minister.