Millions of Greeks are voting in a crucial referendum on whether to accept the terms of an international bailout.
The government has urged a "No" vote, but the "Yes" side warns this could see Greece ejected from the eurozone.
"No one can ignore the will of a people," Prime Minister Alexis Tsipras said, after voting. First results are expected on Sunday evening.
Greeks appear evenly divided over the issue, according to opinion polls. Turnout is expected to be high.
The governing radical-left Syriza party has criticised the bailout terms as humiliating. Its leading figures say rejecting the terms could give them more leverage in talks over the country's massive debt.
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 Friday. Banks stayed shut because of capital controls imposed after the expiry of the current bailout programme.
Casting his ballot, Finance Minister Yanis Varoufakis described the referendum as "a holy moment" that "gives hope that the common currency and democracy can co-exist".
What is the referendum about?
Mr Varoufakis earlier told local media that the EU had "no legal grounds" to throw Greece out of the euro.
He separately told Spain's El Mundo newspaper (in Spanish) that the tactics of Athens' creditors amounted to "terrorism", because they had tried to instil fear in the people by forcing the closure of banks.
Mr Varoufakis said that the banks in Greece would reopen on Tuesday, whatever the outcome, and that Greek Prime Minister 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."
Ballot paper question
"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 programme and beyond" and the second "Preliminary debt sustainability analysis".
Voters must check one of two boxes - "not approved/no" or, below it, "approved/yes".
Electoral workers have raced to get polling stations ready in time, with army helicopters being used instead of boats to rush ballot papers to the islands. Nearly 10 million people are eligible to vote.
Several European officials have complained in strong terms about Greece's abrupt decision to hold a referendum on the terms of a bailout offer they say is no longer on the table.
Greece's Syriza-led government was elected in January on an anti-austerity platform.
The European Commission, the European Union's executive arm - one of the "troika" of creditors along with the International Monetary Fund and the European Central Bank - wants Athens to raise taxes and slash welfare spending to meet its debt obligations.
Credit: The BBC http://www.bbc.com/news/world-europe-33399718