Greece reached a cash-for-reforms deal aimed at avoiding a debt default and an exit from the eurozone.
However, many restrictions remain, including a block on money transfers abroad, and Greeks also face price rises with an increase in Value Added Tax (VAT).
Meanwhile, Germany has said it is prepared to consider further debt concessions to Greece.
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 a day, a restriction imposed amid fears of a run on banks.
From July 20, the daily limit becomes a weekly one, capped at €420, meaning Greeks will not have to queue every day.
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.
However, 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 €86 billion bailout.
Members of PM Alexis Tsipras’ party rebelled against the austerity measures demanded by creditors when it was voted through parliament.
It paved the way for Greece to receive a bridging loan, which enables the reopening of the banks and for Athens to repay debts of €4.2 billion, (including €700 million in interest), to the European Central Bank (ECB) due on July 20.
Both Greece and the IMF have been arguing for a restructuring of its €320 billion debt, saying its current position is “unsustainable”.
German Chancellor Angela Merkel ruled out “a classic haircut” – a markdown of Greece’s debts.
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 program are worked out.
Angela Merkel 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 Angela 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, Wolfgang Schaeuble suggested Greece could temporarily leave the eurozone while it stabilizes its economy.
PM Alexis Tsipras, who has reshuffled his cabinet to replace rebellious ministers, has another set of reforms to push through parliament on July 22.
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