But does the fate of Greece matter to the wider world? Does it matter if Greece eventually leaves the eurozone, or even the European Union?
The short answer is yes. Most people care about the fate of Greece, and hope that it can maintain stability and feel secure.
Many people, but by no means all, believe that its membership of "Club Europe" is one guarantee of a stability which has so often been denied to Greece in the past.
For at least the past hundred years, Greece has swung between democracy and dictatorship, between civilian and military rule, and the outside world would like to be sure the pendulum now stays firmly in the position marked "democratic, civilian government".
Both history and geography help explain why Greece matters far beyond its borders.
The society which gave the world the embryo of modern democracy in Ancient Greece has only enjoyed 40 years of continuous parliamentary democracy in modern times. The days of the "Greek colonels" are still in the not-very-distant past. The last military regime in Athens was overthrown in 1974.
Thirty years earlier, in 1944, Winston Churchill and Joseph Stalin, as uncomfortable wartime allies against the Nazis, were carving up the Balkans between East and West for the post-war era. In Moscow, Churchill put it to Stalin: "Let us settle about our affairs in the Balkans."
Britain's wartime leader wrote down his proposals in pencil on a sheet of paper:
A couple of later additions and amendments in red ink are important.
The Greece section is changed so that "the others 10%" becomes "Russia 10%".
And after Great Britain's claim to 90% influence has been added the words "in accord with USA", recognising where the real post-war power would lie.
It was part of the far larger, so-called "percentages agreement" attempting to parcel out Yugoslavia, Bulgaria and Hungary too. There's a blue pencil tick near the top of the page, apparently in Stalin's hand.
He may have honoured that limit to his influence in Greece, but certainly not his apparent agreement to share Hungary and Bulgaria.
After that, Churchill moved very swiftly to try to ensure that the Greek Communists - who had been such a strong force in the divided Resistance to Nazi occupation - would not prevail.
He made a dangerous flight to Athens on Christmas Day, 1944, and on 26 December posed with the Greek Orthodox Archbishop Damaskinos of Athens.
Churchill backed him as regent, or temporary head of state, ahead of Greece's descent into the nightmare of civil war between communists and anti-communists.
That civil war is called by some the first battle of the Cold War.
If you accept that another contest for influence between Vladimir Putin's Russia and the West is now under way, it's not hard to see why anything like "Grexit", which would detach Greece from the inner core of EU states, alarms not just fellow European leaders, but also the United States.
President Putin has been courting the Greek Prime Minister, Alexis Tsipras. It's true that the Russian leader has offered only limited financial support.
But some experts see real opportunities for Russia either way: if the Greek marriage to the EU were to end in a messy divorce or if Greece stays in but continues to hedge its bets through friendship with Moscow.
The most imaginative commentators even suggest that if Greece left the EU it would then be bankrolled by Moscow in exchange for Greek agreement to resign from Nato as well, allowing Russian warships to sail unhindered through Greek waters into the Mediterranean.
Even if that seems far-fetched, there's little doubt Mr Putin would see himself as the winner if Greece became either semi-detached or wholly detached from the European Union and perhaps permanently destabilised. Anything which hurts the European Union can look like an advance seen from the Kremlin.
A brief look at an atlas reminds us why Churchill wanted to be sure of Greece.
Greek territory controls a huge area at the north-eastern corner of the Mediterranean. Its territory includes several hundred islands in the Aegean, Ionian and Mediterranean Seas.
Greece forms the southern tip of the Balkan Peninsula.
It is the cornerstone of south-eastern Europe, even if Cyprus is now the furthest outpost of the EU in that direction.
It didn't take very long after the restoration of democracy to Greece in 1974 for the country to be welcomed into the European Union in 1981.
That was meant to be a decisive turning point, cementing Greece into political and social stability.
When the question of Greece joining was debated in the House of Commons in 1979, one of the senior Foreign Office ministers in Margaret Thatcher's first government, the Lord Privy Seal, Sir Ian Gilmour, spoke approvingly of: "...the political significance of accession, the endorsement which it represents of Greece's democratic progress and of her decisive orientation towards Western Europe. But economically, too, accession will be of great importance to Greece. It will be a challenge and an opportunity."
Greece's membership has certainly proved to be a challenge as well as an opportunity.
1941: Greece falls to Germany in World War Two.
1944: British and Greek forces combine to force Nazi withdrawal. With backing from Britain, Georgios Papandreou becomes prime minister. Communists protest. Tensions rise and there is sporadic violence.
1946-49: Royalist parties win elections. Ensuing civil war ends with defeat of communist forces.
1952: New constitution declares Greece a kingdom ruled by parliamentary democracy. Greece joins Nato.
1967: Group of army officers seize power in military coup.
1974: Dictatorship ends, after a Greece-backed coup against President Makarios of Cyprus is followed by Turkish invasion and occupation of north of the island.
1975: New constitution declares Greece a parliamentary republic with some executive powers vested in a president.
1981: Greece joins EU.
2002: Euro replaces drachma.
More key events in Greece's history
Greece country profile
We know that the Greek agony is not over - the country's future is still hugely uncertain.