London (CNN) Citizens from 28 countries will cast their votes in European parliamentary elections this week in what many politicians say could be one of the bloc's most pivotal moments.

The election will determine the future direction of the European Union itself as it confronts the threat of nationalists and populists across the continent, and as the drawn-out Brexit process continues to dominate the political agenda.

Around 350 million people across the EU are eligible to cast ballots for the 751 members of the European Parliament (MEPs), who pass hundreds of laws each year -- from how many hours employees work, to the quality of air that citizens breathe, and even data privacy.

While historically turnout has been relatively low, this year analysts say voters are much more engaged with the poll, which runs from May 23 to 26. As a result, Europe's Parliament is expected to undergo a major shake-up.

Members of the European Parliament take part in a session in Strasbourg in 2018.

Populists expected to make big gains

Parliament's largest groups, the center-right European People's Party (EPP) and the center-left Progressive Alliance of Socialists and Democrats (S&D) -- who have long enjoyed a joint majority in Parliament -- are expected to lose a number of seats with euroskeptic and populist movements tipped to make big gains this year.

Senior research fellow Camino Mortera-Martinez from the Center for European Reform (CER) argues that while those ascendant political groups may not dominate Parliament, their presence will be felt as they apply pressure and complicate EU decision-making.

"Euroskeptics and populists are going to grow exponentially this time," she says. "You're going to have a much more divided Parliament. It's going to be more difficult to find compromises."

Mortera-Martinez says there was always going to be a surge in populist parties following the migration crisis eurozone woes and various terrorist attacks across the continent.

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In April Italian Deputy Prime Minister Matteo Salvini -- who has spearheaded a series of anti-immigrant policies -- launched what amounted to a "Make Europe Great Again" campaign in an attempt to unite far-right political parties across the continent ahead of the elections. The newly formed alliance hopes to form a weighty bloc in Parliament -- the third largest, Marine Le Pen of France's National Rally has predicted.

According to Matthew Goodwin, a professor of politics at the UK-based University of Kent, many European populists believe they will be able to influence Europe from the inside out.

Goodwin previously told CNN that populists will be a "disruptive political force" and will most likely push "for the return of powers to nation states, stronger border security, more help with dealing with refugees and probably more democratic and transparent institutions."

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However, Mortera-Martinez suggests that populists, nationalist and euroskeptic parties will ultimately struggle to work together "so their influence will diminish a lot because of the lack of coordination."

In a fragmented Parliament, Europe's Greens -- on course for their best-ever showing -- could find themselves wielding more power. With support for mainstream parties declining, the votes of their projected 57 or more MEPs may well be key to any moderate, pro-EU alliance.

The elections that weren't supposed to involve the UK

Brexit is also another major factor this year. The UK was scheduled to leave the European Union on March 29, but missed that deadline and another in April, meaning it is now obliged to take part in elections. If Brexit does occur soon though, British MEPs won't take up their seats.

"I think this whole Brexit uncertainty will not only have a role in the elections but also in the priorities of the next commission," Mortera-Martinez says.

"Within the next five years the question of how to accommodate the UK -- in, and out of Europe -- is going to take up a lot of time for the leaders of the European Commission."

It's also an opportunity for remainers and leavers to express their frustrations, Agata Gostyńska-Jakubowska, also a senior research fellow at the CER, said in a statement.

"Prime Minister Theresa May's Conservatives, which had hoped to avoid holding these elections, are facing a drubbing at the hands of Nigel Farage's new Brexit Party," she noted, adding that parties pushing to prevent Brexit are "likely to perform well and keep up the pressure for another referendum on the UK's membership of the EU."

"If anything, these European elections will confirm that the UK remains as divided over Europe as ever," Gostyńska-Jakubowska added.

Prime Minister Theresa May had hoped that the UK would avoid holding these elections.

While MEPs have previously struggled to communicate to voters what they actually do at the complex institution, Mortera-Martinez says Europeans are taking a greater interest in the elections this time around.

"Back in 2014 no one thought about the European Union much," she says.

But this year "so many people actually know the elections are happening," she says, "and that there is something at stake."

This story has been updated to correct the number of eligible EU voters.