Matteo Salvini, Italy’s deputy prime minister and leader of the right-wing Lega party, rallied in Milan on Saturday with a who’s who of far-right, nationalistic, anti-immigrant European leaders.

The guest list included Marine Le Pen, of France’s National Rally (formerly the National Front), and Geert Wilders of the Netherlands’ Party for Freedom. They were making the case for why politicians and parties deeply skeptical of the European Union should be elected to the European Parliament in the elections starting May 23.

“There are no extremists, racists, or fascists in this square,” Salvini told the thousands of supporters who’d gathered in the central square in Milan. “Here you won’t find the far-right, but the politics of good sense. The extremists are those who have governed Europe for the past 20 years.”

Euroskeptic parties have always existed within the European Parliament. But they’ve struggled to wield substantial influence. Their staunchly nationalistic views aren’t exactly a successful formula for cooperation in the pan-European political body.

But the current crop of far-right leaders are trying something different this year: attempting to build a cross-continent alliance of anti-EU parties. They’re betting that by working together, they can weaken — and remake — the EU from within.

Salvini, who’s framed himself the de facto leader of this coalition, has embraced the slogan “Towards a Common Sense Europe.” Besides Le Pen’s National Rally and Wilders’s Party for Freedom, other far-right parties have joined the cause, including Germany’s Alternative for Deutschland (AfD) and Austria’s (currently scandal plagued) Freedom Party. Broadly, these leaders want to curtail immigration. They may want to reorient the EU’s priorities on the global stage, too.

But, mostly, they want to elevate the sovereignty and economic interests of individual member-states over the collective interests of the EU.

“In a way, it’s kind of the ultimate irony — that parties who are pushing for power to stay at the national level are seeing a utility in working together, and in their campaigning around these elections,” Susi Dennison, a senior policy fellow at the European Council on Foreign Relations, told me.

But even if the far-right succeeds in these European elections, it’s not clear whether these parties will be able to translate their campaign slogans into workable politics.

They’re also not going unchallenged. For example, French President Emmanuel Macron is trying to promote his vision of a stronger EU along with a coalition of liberal and centrist parties.

The question is, who’s vision will win out — and where in Europe the far-right’s message will resonate the most — as more than 400 million voters in all 28 EU member-states are eligible to cast ballots in the world’s second-largest election.

Here’s what to know about the European Parliament and what’s at stake in these upcoming elections.

What is the European Parliament and why does it matter?

The European Parliament is one of the legislative bodies of the EU, and the only one whose members — known as MEPs — are directly elected by EU citizens. MEPs serve five-year terms, which will start this July.

There are currently 751 MEPs serving in the European Parliament, though it will decrease when/if the UK leaves the European Union. The amount of representation depends on the size of EU countries. Germany gets the most at 96 MEPs; Malta only gets six.

European elections are organized on the national level, so MEP candidates are often affiliated with domestic political parties or organized around national issues.

Once MEPs are elected to the European Parliament, they join together in bigger groups based on where they fall on the political spectrum. For example, center-left MEPs may run as Labour Party candidates in the UK, Socialist Worker’s Party (PSOE) candidates in Spain, and Social Democratic Party (SPD) candidates in Germany. But once they arrive in Brussels, they all sit together as the Party of European Socialists.

The same is true on the center-right, which is called the European People’s Party (EPP), and is currently the largest bloc out of the eight that exist. Some MEPs don’t sit with anyone and kind of hang out by themselves. But, ideally, these political groupings are supposed to promote the unity of political ideology over nationality.

How the European Parliament is organized ultimately helps determine its influence alongside the other bodies of the EU — specifically the European Commission and the Council of the European Union.

The European Parliament can approve (or reject) legislation — including trade deals, and, someday, the Brexit deal — alongside the Council of the European Union, which is made up of government ministers from the individual member-states.

The European Parliament cannot independently introduce legislation, though. That’s the job of the European Commission, which is basically the equivalent of the EU’s executive branch and is the body’s most powerful institution.

The EU’s decision-making is often a negotiation among the interests of the Commission, the Council of the European Union, and the European Parliament, Olivier Costa, an EU expert and professor at the College of Europe, told me.

But the European Parliament does have a role in shaping the direction of the EU. It must, for example, approve or reject an EU budget — and that’s no small political cudgel. The European Parliament also approves the president and appointees to the EU Commission, and must do so with the European election results in mind, meaning that the leadership at the top often reflects the makeup of the MEPs.

That’s why the far-right’s attempts to organize are so profound. It’s one thing if a bunch of Euroskeptics win a few scattered seats in the European Parliament, but if they can gain more robust support and potentially pull voters away from more centrist parties, they can play a spoiler role, slowing down legislation. They may have leverage to help shape what the EU spends money on and who sits on the Commission.

“You would begin to see a real change in the DNA of the EU if this kind of anti-European view gets inside the executive body of the EU,” Dennison said.

What does the far-right see in Brussels? An opening to power, and a platform.

Euroskeptic parties have always been elected to the European Parliament — and it’s not exclusively a far-right phenomenon, either.

Sometimes, when it comes to EU politics, the fringier and more far-out, the better — and this year is no different. The UK (which wasn’t supposed to be participating in these elections at all) has a list of candidates that includes a YouTuber known as Sargon of Akkad and a virulent Islamophobe known as Tommy Robinson. In Italy, disgraced former prime minister Silvio Berlusconi is trying to make a political comeback; Mussolini’s great-grandson is also running. His cousin, Mussolini’s granddaughter, was elected MEP in 2014.

You get the idea.

The barrier to run for European Parliament is a lot lower in most countries than in national elections, so if you’re a small, anti-establishment party, it’s much easier to run for MEP than, say, a seat in your home country’s parliament.

There’s a lot less at stake for many voters, too, so they might be willing to risk a protest vote since no one party actually wins the European Parliamentary elections outright. MEPs aren’t exactly as high profile as national political figures, either, which means they’re not being vetted as closely. (A UK survey in 2014 said only 1 in 10 voters in the country could name a single MEP.) And since turnout tends to be low — it was just 42.6 percent across Europe in 2014 — it tends to motivate more passionate voters, and that may include those with a grievance.

But the European Parliament can be a great backdoor into mainstream national politics, which is why it often attracts upstarts. Becoming an MEP confers a degree of legitimacy. It provides a political platform. And there’s good money in it — including resources and salaries for professional staff.

For instance, John Curtice, a politics professor at Strathclyde University, told me the “European Parliament has been a godsend” to the UK Independent Party (UKIP) — the Euroskeptic party that championed Brexit.

But being elected to the European Parliament doesn’t guarantee you’ll have influence once you get there, even for far-right or Euroskeptic parties. Traditionally, they’ve had different agendas, tagged on to bigger groups, or simply floated alone, which diluted their power and influence.

That’s precisely what these far-right Euroskeptic leaders want to change in 2019.

“For the first time, it seems that the extreme right people are organizing themselves a little bit better,” Costa said. “So there is the possibility of the creation of one single, large Euroskeptic group of the right wing of the European Parliament.”

What do they actually want to do once they get there?

The goal of these far-right Euroskeptics isn’t really to destroy the Europe Union from within, but to try to remake and reorient the bloc, starting with more influence in the European Parliament in 2019.

Kalypso Nicolaïdis, a professor of international relations at the University of Oxford and author of a new book on Brexit, described this as the number of “transformative Euroskeptics” increasing compared to the “existential Euroskeptics.”

There’s a few reasons for this. For one, there’s Brexit — or, more accurately, the lack thereof. The United Kingdom’s divorce from the EU has become a messy and drawn-out affair and that’s soured many Euroskeptics in other parts of the continent from pursuing similar exit movements.

Also, support for the EU itself is fairly strong among many European voters — though they’re souring a bit on the direction of the EU experiment and on the European Parliament as an institution. In a Eurobarometer survey in April, 68 percent of respondents said they believe EU countries have, overall, benefited from membership in the bloc — but 50 percent of people in the same survey also said that they didn’t feel as though the EU was going in the right direction.

A Pew survey from 2018 found a median 62 percent in 10 EU countries approved of the EU as a whole, but that only a median of 50 percent approved of the European Parliament.

Far-right Euroskeptics are trying to appeal to those dissatisfied with the status quo. “They’re positioning themselves as the parties of change,” Dennison said, “but within still the bigger European idea.”

So this isn’t opposition to the existence of the European Union. It’s opposition to the European Union as it exists now, at least according to the far-right skeptics: too powerful, too progressive, too multicultural.

“They think, ‘This is not our Europe,” Costa told me of the far-right groups. “Our Europe is a Christian Europe, a white Europe, based on the family, traditional values, the role of woman and the role of man.”

It’s not anti-Europe versus pro-Europe but of what kind of Europe it will be. And one way to help shape that future is gaining strength in the European Parliament.

The European Parliament is supposed to be about Europe. But domestic politics still creep in.

The far-right populists will almost certainly make gains in the European Parliament in the upcoming elections. They probably won’t win a majority, but they could diminish the majorities held by the center-left and center-right. And some experts say it’s possible that the far-right could claim up to a third of the seats.

But how well they do will probably have more to do with what’s going on in France or Germany or the UK than what’s going on in the EU. This is the other irony, or maybe the worst-kept secret of the European Parliamentary elections: They are very much a referendum on national politics.

The obvious example is the UK, where the European elections are a proxy for the Brexit debate. Former UKIP leader Nigel Farage and his new Brexit Party, whose main campaign platform is that the UK should leave the EU, are leading in the polls in the UK. Remainers (people who want the UK to stay in the EU) will likely split the vote, but many are decamping to the Liberal Democrats. And Conservatives — Prime Minister Theresa May’s party in power — are expected to come in sixth place, unable to shake the stench of a botched Brexit.

Similar dynamics are playing out in other countries. In Austria, a scandal involving a far-right politician has just brought down the government, which might end up damaging the strength of the far-right Freedom Party at the polls in the European Parliament elections.

In France, the European Parliamentary race has turned into a rematch of the 2017 presidential election, though this time President Macron’s centrist République En Marche party might be bested by Le Pen’s National Rally. Macron is the main figurehead for closer European integration, but his message has been muddled and his image damaged in the wake of the yellow vest protests that have rocked his country for months.

This isn’t to say that voters don’t care about the EU; obviously, they do. It’s just that how they see it tends to be colored by their own domestic political debates. Some MEP candidates are a trying to change that — Volt, a party founded in 2017, is running as the only transnational European party, though right now it’s only on the ballot in eight EU countries. And voters tend to elect MEPs who say they’ll represent their country’s national interest in the European Parliament.

Which is why the far-right might have an easier time winning seats in the European Parliament than they will executing on their policies once they’re elected. Broadly, these far-right parties want less immigration, more emphasis on national sovereignty, and some reorientation of priorities, including on foreign policy.

These elections have given the impression that they’re a force to be reckoned with, Dennison said. But “there are huge differences between these parties in terms of their agenda, and there are absolutely no guarantees that they will work together once they’re inside the Parliament.”

Take immigration: Most nationalist parties want to limit immigration, but how to do that — and how limited it should be — is up for debate. As a German Green Party member pointed out in an interview with an Italian media outlet, Italy’s Salvini wants to redistribute refugees across EU member-states. The leading candidate for Germany’s AfD party, on the other hand, “doesn’t want a single refugee.” Salvini’s Lega and AfD are allies now; but what happens when they’re in the European Parliament together?

Another area of disagreement is Russia. Salvini and Le Pen are both very friendly with Russia and see Russian President Vladimir Putin as an ally (Salvini even once creepily wore a Putin shirt). But other far-right leaders from European countries a little closer to Russia on the map don’t share that sentiment. “We are very concerned about Russian aggression. A wounded bear is dangerous,” an MEP in the far-right Danish People’s Party told the Guardian last month.

These disagreements are not small, and they have long hobbled the far-right in the European Parliament. Costa told me he doubts they’ll ever become truly organized. “Each time we have a group of the extreme right [in Parliament], they would fight,” Costa said.

But, he added, the fact that they have all decided to work together has symbolic importance. The rise of Euroskeptic parties matters, even if the scope of their influence is still untested.

And they’re tapping into something across the continent. “The case for the European project is still there,” Dennison told me. “But the current version of it is really not inspiring voters right now.”