Greeks are voting in a controversial referendum on whether to accept the terms of an international bailout.
Polling stations opened at 07:00 local time, with the first results expected in the evening.
The government has urged a “No” vote, but opponents warn this could see Greece ejected from the eurozone.
Greeks appear evenly divided over the issue, according to opinion polls. Turnout is expected to be high, after a frenetic week of campaigning.
“No one can ignore the determination of a people taking its destiny in its own hands,” PM Alexis Tsipras said, after casting his ballot on July 5.
However, international creditors have warned that a “No” vote could choke off vital funding for Greek banks and lead to “Grexit – a chaotic departure from the common European currency. The “Yes” campaign has framed the vote as a referendum on Greek membership of the eurozone.
Supporters of both sides held rallies in Athens on July 3. Banks stayed shut because of capital controls imposed after the expiry of the current bailout program.
Greek Finance Minister Yanis Varoufakis told local media on Saturday that the EU had “no legal grounds” to throw Greece out of the euro.
On the eve of the referendum, Yanis Varoufakis accused Athens’ creditors of trying to sow fear around the vote. He told Spain’s El Mundo newspaper: “Why did they force us to close the banks? To instil fear in people. And spreading fear is called terrorism.”
Yanis Varoufakis said that the banks in Greece would reopen on July 7 whatever the outcome and that PM Alexis Tsipras would still reach an agreement with creditors if the result was “No” in the referendum.
Meanwhile, German Finance Minister Wolfgang Schaeuble, one of Greece’s harshest critics, suggested that if Greece were to leave the eurozone, it might only be temporary.
“Whether with the euro or temporarily without it: only the Greeks can answer this question,” he told the German newspaper Bild.
“And it is clear that we will not leave the people in the lurch.”
The referendum question is: “Must the agreement plan submitted by the European Commission, the European Central Bank and the International Monetary Fund to the Eurogroup of 25 June, 2015, and comprised of two parts which make up their joint proposal, be accepted? The first document is titled <<Reforms for the completion of the current program and beyond>> and the second <<Preliminary debt sustainability analysis>>.”
Voters must check one of two boxes – “not approved/no” or, below it, “approved/yes”.