Greeks are voting in a general election which could result in Greece trying to renegotiate the terms of its bailout with international lenders.
The leftwing Syriza party, which is tipped to win, wants part of Greece's huge debt written off and austerity measures revoked.
This has spooked money markets and raised fears of a Greek exit from the euro.
But the governing New Democracy party says the economy is recovering.
Greece has endured tough budget cuts in return for the bailout negotiated with the so-called troika of lenders - the European Union, International Monetary Fund (IMF) and European Central Bank (ECB).
The economy has shrunk drastically since the 2008 global financial crisis, increasing unemployment and throwing many Greeks into poverty.
Polls across Greece opened at 07:00 local time (05:00 GMT) and will close at 19:00.
There are nearly 10 million eligible voters, who are electing the country's 300-member parliament.
First exit polls are expected immediately after the voting ends.
Syriza leader Alexis Tsipras says his party will restore "dignity" to Greece by rolling back on cuts to jobs, pay and pensions which have hurt millions of people across the country.
The possibility of a Syriza victory has sparked fears that Greece could default on its debt and leave the euro - the single currency of 19 EU members.
This is despite the fact that Syriza has moderated its stance since the peak of the eurozone crisis, and says it wants Greece to stay a member of the currency.
Meanwhile, the leader of centre-right New Democracy and PM Antonis Samaras has promised to work "day and night" to keep the country standing.
Syriza, he argues, could force the country from the euro by its policies, serving what he called the "drachma lobby", a reference to the former Greek currency.
He also warns that Greece could miss out on a massive programme of quantitative easing unveiled by the ECB last week to help stimulate the eurozone economy.
The centrist To Potami and the right-wing Golden Dawn party are expected to fight for third place in the elections.
