Barring a huge upset, victory for Syriza, which has led opinion polls for months, would produce the first government in the eurozone openly committed to cancelling the austerity terms of its EU and IMF-backed bailout programme.
A Syriza win would represent another turning point for Europe after last week's announcement by the European Central Bank of a massive injection of cash into the bloc's flagging economy after years of trying to clamp down on budgets and pushing countries to pass structural reforms.
Polls are due to close at 1700GMT with the first exit poll expected immediately after voting ends. Nearly 9.8 million Greeks are registered to vote in the election.
"Syriza's attitude to this election has been that they will go up against Europe," reports from Athens said.
"The election is expected to bring in a government led by the left-wing Syriza party, at a time of economic crisis"
Turton also reported that while Syriza's policies have appealed to many groups hit by the economic crisis facing Greece, one group in particular is the youth, among whom as many as 50 percent are unemployed.
While Syriza is expected to form the biggest group in the 300-seat parliament, it is unclear if it will be able to govern alone or have to form a coalition with one or more of the smaller parties. Final polls on Friday gave the party led by 40-year-old Alexis Tsipras a lead of up to 6.7 points with 31.2 to 33.4 percent of the vote, close to the level needed for an outright victory.
Three out of four polls showed Syriza widening the gap over the centre-right New Democracy party of Prime Minister Antonis Samaras.
After its most severe crisis since the fall of its military government in 1974, Greece's economy has shrunk by some 25 percent, thousands of businesses have closed, wages and pensions have been slashed and unemployment among young people is over 50 percent.
At the same time, its massive public debt has climbed from 146 percent of gross domestic product in 2010 to 175.5 percent last year, the second highest in the world.