Members of the Greek Communist Party attend an anti-austerity rally at Syntagma square on June 26, 2015 in Athens, Greece. The Greek government offered a series of measures this week, including multiple tax increases, to persuade its creditors to release bailout funds and keep the country from defaulting on its debts as soon as next week. Photo by Milos Bicanski/Getty Images

Yet again, the Greek debt crisis is reaching a boiling point. On Tuesday night, Greece missed a debt repayment to the International Monetary Fund, putting it in a league with Zimbabwe and Somalia.

Meanwhile, the leftist Syriza government has called a public referendum this Sunday over whether Greece should abide by creditors’ harsh demands or refuse and chart its own course -- a course that could take it out of the eurozone and into uncharted waters.

As Greece and its European counterparts scrap over yet another proposed compromise, it’s worthwhile to step back and appraise how Greece got to this point -- and what’s next.

How did Greece pile up so much debt?

When Greece joined the eurozone in 2001, optimism reigned. Joining Europe’s currency union made Greece attractive to foreign investors. Economic growth topped 4 percent in the mid-2000s.

But Greece was running up unsustainable debts. Public-sector employees enjoyed generous pensions and retirement in their 50s. Workers received infamous 13th and 14th month salaries -- double pay around the holidays. Profligate as public spending was, however, pensions and salaries have become scapegoats for deeper issues plaguing Greece, political corruption and widespread tax evasion among them.

All of this, of course, was enabled by low-interest loans from creditors. Banks were content to look past Greece’s weaknesses and continue extending profitable loans throughout the 2000s.

Like most of Europe, Greece took a serious economic hit during the global financial crisis of 2007-2009. But in 2009, Greece admitted things were worse than they seemed: Deficits had reached 12.7 percent of GDP, four times the limit imposed by the European Union. Something had to give.

Who bailed them out?

With its debt woes exposed to public view, the Greek government suddenly found it impossible to raise funds and finance old debts. Prodded by the EU, Prime Minister George Papandreou imposed major cuts to the public sector alongside steep tax hikes. Although polls showed wide support for the austerity programs, thousands took to the streets in waves of strikes and protest.

In 2010, a trio of European and international governing bodies known as the troika hammered out an agreement to direct $143 billion in bailout loans to Greece. A second bailout totaling $170 billion followed in 2012, tied to tougher austerity measures.

The troika consists of the European Central Bank, the International Monetary Fund and the European Commission, the central governing body of the European Union.

Why didn’t the bailouts solve anything?

The massive loans allowed Greece to stay afloat (if barely), but successive bouts of mandatory austerity measures sent the Greek economy spiraling into depression. Economic output has plunged 25 percent and employment sunk by a quarter since 2010.

As the IMF later admitted, the architects of the bailouts drastically underestimated the impacts of budget cuts and tax increases. The IMF predicted that by 2012, for instance, Greece would see positive GDP growth. Instead, the economy sank 7 percent. Today, more than 60 percent of Greek children are at risk of poverty.

Who or what is Syriza?

Widespread dissatisfaction in Greece led to the rise of Syriza, what had been a relatively fringe left-wing socialist party. In January, 2015, Syriza pulled off a stunning electoral victory, propelling the charismatic 40-year-old Alexis Tsipras to prime minister and the self-described “erratic Marxist” Yanis Varoufakis to finance minister.

Syriza won public approval in part by promising Greeks an end to austerity and a repudiation of creditors’ hard-nosed demands. But as Varoufakis and Tsipras have learned over six months of white-knuckle negotiations, the Troika is no pushover.

What do the creditors want?

In short, money. They want Greece to continue making debt repayments and abiding by structural reforms to its government and economy. These include not just public-sector cuts, but privatization of national industries and measures to stem tax evasion.

But more broadly, the troika wants to maintain power. If Greece bucks its creditors' demands, other troubled economies might follow suit. Spain, Italy and Portugal are all considered flight risks -- though to a far lesser degree than Greece.

A break-up of the eurozone would spell disaster for the central European political project of the last two decades. It would particularly pain Germany, which has served as the eurozone’s financial anchor. As Greece has found out, German finance minister Wolfgang Schaeuble and prime minister Angela Merkel are unwilling to budge a centimeter for fear of losing that upper hand.

So, did Greece default?

If you ask the IMF, Greece went into "arrears" when it missed its 1.5-billion-euro payment Tuesday. But functionally, that means default. Greece is the first country to win that dubious distinction since Zimbabwe in 2001.

The consequences aren’t quite as severe as if Greece had defaulted to private banks, however. Credit-rating agencies don’t consider IMF debts to be private debts, so Greece won’t take another hit to its foundering credit rating.

What’s next?

The international commentariat has seized on “grexit” as the favored term for a Greek exit from the eurozone. Why would Greece want to leave the euro? The simplest answer is monetary autonomy. In the past, Greek central bankers could have devalued their former sovereign currency, the drachma, to help wiggle out of crushing debt. Central banks can always print more money.

But no such option exists in the eurozone. That has put Greece in a Scylla-and-Charybdis position: Either it accepts painful austerity measures or risks a potentially costlier break from the eurozone. Prime Minister Tsipras has urged his fellow citizens to vote "oxi," or no, on the referendum, hoping to win a democratic mandate to rebuff the troika's demands.

Tsipras said he would resign if Greeks voted "yes." Varoufakis told Bloomberg he'd sooner cut off his arm than sign an unfavorable agreement.

But the past week's dueling demonstrations over the referendum -- "no" on Monday, "yes" on Tuesday -- showed there’s no easy answer.

What does all this mean for American investors?

Unless you’re busily speculating on Greek government bonds or European stock futures, you shouldn’t worry too much in the short term. The European Stability Mechanism was established in 2012 by 17 states to contain the potential fallout from a total Greek default with a "firewall" of capital cushions.

A mortal blow to the eurozone, however, could prove dangerous to the global financial system. The eurozone makes up 20 percent of the world’s economic output. Multi-trillion-dollar bond markets are already touchy, and European dislocation could send them into freefall, affecting millions of Americans’ pension fund investments and retirement accounts.

For now, however, neither Greece nor the troika has signalled a firm wish to part ways. But neither have they found a wide enough common ground to fit both Syriza’s political promises and European finance minister’s demands.