Greece has endured tough budget cuts in return for its bailout, negotiated with the European Union, International Monetary Fund (IMF) and European Central Bank (ECB).
The economy has shrunk drastically since the 2008 global financial crisis, and increasing unemployment has thrown many Greeks into poverty.
A Syriza win is 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.
Greeks 9.8 millions are registered to vote in the election.