Sunday, Greek voters go to the polls to elect a new government. The outcome of the election could determine whether Greece stays in the euro or not. Which means the fate of Europe — and the global economy — just might hang in the balance. No pressure or anything! Here’s a primer:

Supporters cheer New Democracy party leader, Antonis Samaras, during the party's main pre-election rally in the central Athens Syntagma square on June 15, 2012. (Louisa Gouliamaki/AFP/Getty Images)

So what are the choices facing Greek voters? At the moment, there are two main parties vying to head up the parliament. The leading conservative party, New Democracy, helped negotiate the original bailout deal with the troika back in February and has promised to “find common ground” on the agreement, albeit with some modifications to ease the pain for Greece. The other front-runner is a coalition of leftist parties, Syriza, whose leader, Alexis Tsipras, has rejected the troika agreement and wants to revamp it entirely.

What happens if New Democracy wins? New Democracy’s leader, Antonis Samaras will first have to form a coalition government with a variety of smaller parties on the left — not an easy task — and then figure out a way to make the troika agreement work. Already, euro zone officials have said they are open to small modifications to the deal, from allowing Greece slightly more flexibility to repay its loans to offering money for infrastructure projects in Greece. If Samaras can reach an agreement that pleases all sides, that could enable Greece to stay within the euro (though the country would still be facing years of hardship, austerity and weak growth).

What happens if Syriza wins? That’s far more uncertain. While Syriza leader Alexis Tsipras has said that he wants Greece to stay in the euro, it’s unclear if he can make that work. For one, analysts say, Syriza will likely have difficulty forming a coalition government. And even if Tsipras can pull that off, many elements within his coalition are demanding a radical renegotiation of the bailout agreement — which might cause the troika to balk and stop sending money to Greece. In the worst case, the country would face a cash crunch, and Tspiras would have little choice but to nationalize the banks and introduce a new currency.

Would an exit from the euro really be a calamity? Many economists seem to think so. A Greece exit from the euro would likely be accompanied by a collapse of the domestic banking sector and steep inflation. “Greece would be forced into a crisis many times more severe than its present one, further fueling social unrest,” five Greek economists warned Friday in the Wall Street Journal. Perhaps more significant still, a Greek exit could accelerate bank runs in other troubled euro countries like Spain and Italy, as investors and depositors got nervous that those countries might be next to leave. A total collapse of the currency union would suddenly look like a real possibility.

So is there any hope Greece will pull through? Perhaps — though it won’t be easy. Elias Papaioannou, a Greek expert at Dartmouth College, points out that even if New Democracy wins on Sunday, several things will need to happen to calm the panic. First, the troika will need to be willing to relax the terms of the bailout agreement in order to placate Greek voters. (One possibility? Offering money to finance expanded unemployment insurance in Greece.) Second, the new Greek government will have to figure out how to rebuild Greek’s battered banking sector in order to jumpstart growth. And third, euro zone officials will have to restore confidence in the entire euro zone — not just in Greece, but in troubled countries like Spain as well.

“Greece’s biggest problem right now is not austerity per se, although that’s a problem,” Papaioannou says. “The biggest problem is uncertainty about the future of the currency. That’s impeding investment. If that larger uncertainty isn’t resolved, none of these plans [to modify the bailout agreement] will work.”

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