Greek banks are reopening after being closed for three weeks because of the deadlock over the country's debt, as the government initiates repayment of its loans to the ECB and IMF.
Athens reached a cash-for-reforms deal aimed at avoiding a debt default and an exit from the eurozone.
But many restrictions remain and Greeks also face price rises with an increase in Value Added Tax (VAT).
Germany has said it may consider further debt concessions to Greece.
Greece was making a €4.2bn (£3bn) payment due to the European Central Bank (ECB) on Monday, as well as €2.05bn in arrears to the International Monetary Fund (IMF).
The IMF later confirmed the money had been paid and that Greece was "therefore no longer in arrears".
Queues at ATMs have been a feature of life in Greece for weeks, with people waiting in line each day to withdraw a maximum of €60 (£41) a day, a restriction imposed amid fears of a run on banks.
From Monday, the daily limit becomes a weekly one, capped at €420 (£291), meaning Greeks will not have to queue every day.
An architect told the BBC that the banks re-opening will make only a small difference to his ability to operate.
"The key challenge is that we cannot pay our suppliers, which means that we will eventually run out of products to sell," Vassilis Masselos told the BBC World Service's Newsday programme.
Analysis by Robert Peston, BBC economics editor
Just because the doors of Greek banks are open today, don't be fooled into thinking they and the Greek economy are anywhere near back to recovery.
There are still major restrictions on the ability of their customers to obtain their cash or move it around.
The symbolic importance of the European Central Bank turning on the emergency lending tap again was important, but it has only been turned on a fraction.
It has given enough additional Emergency Liquidity Assistance - €900m - to keep the banks alive in a technical sense.
There is no possibility of them thriving for months and even possibly years.
But a block on transfers to foreign banks and a ban on cashing cheques remain in place.
Greeks will also pay more on a range of goods and services, including taxis and restaurants, with VAT rising from 13% to 23%.
The rise was among a package of reforms demanded by Greece's creditors to open talks on the proposed €86bn bailout.
Some members of Prime Minister Alexis Tsipras's party rebelled against the austerity measures demanded by creditors when it was voted through parliament.
But the vote paved the way for Greece to receive a bridging loan, which enabled the reopening of the banks and for Athens to repay debts to its creditors on Monday.
Both Greece and the IMF have been arguing for a restructuring of its €320bn debt, saying its current position is "unsustainable".
German Chancellor Angela Merkel ruled out "a classic haircut" - a markdown of Greece's debts.
But she told German television other forms of relief, such as extending maturities or slashing interest rates, could be considered once the details of the latest programme are worked out.
She also played down reports of a row with her Finance Minister Wolfgang Schaeuble, who suggested in an interview with Der Spiegel magazine that he would rather resign than defend something he did not believe in.
"The finance minister will, like me, conduct these negotiations and I can only say that no-one came to me and asked to be relieved," said Mrs Merkel when asked about the suggestion.
Germany, which is the largest contributor to Greek rescue funds, has taken a tough line on Greece.
At one point in the fraught talks over the bailout, Mr Schaeuble suggested Greece could temporarily leave the eurozone while it stabilises its economy.
Mr Tsipras, who has reshuffled his cabinet to replace rebellious ministers, has another set of reforms to push through parliament on Wednesday.
While banks throwing open their doors marks the return of some normality to the Greek economy, long-term problems remain.
Unemployment is stubbornly high, and as this chart shows, Greece's recession is comparable to one of history's most famous economic crashes.