There has never been so much interest in elections at the European Parliament. For the first time in 40 years, anti-establishment parties are expected to end the dominance of mainstream politics at the European Union. CNBC takes a look at why this election matters for Europeans, as well as investors.

What are European elections?

Citizens from every country in the European Union have the right to choose lawmakers to represent them at the European Parliament — the EU's legislative body and its only directly-represented chamber. This has been the case since 1979. This year's vote takes place from May 23 to 26. MEPs are mostly made up of lawmakers that are associated with established political parties in each member state, for example the U.K.'s Conservative Party. But in the EU Parliament, these MEPs join up into various cross-border political factions according to their political stance. An example is that the liberal parties usually join the of ALDE group (The Alliance of Liberals and Democrats for Europe group). There's 10 of these political groups and they have a say on who is the head of the European Commission — the EU's executive arm.

Members of the European Parliament take part in a voting session at the European Parliament in Strasbourg, eastern France, on June 7, 2016. FREDERICK FLORIN/AFP/Getty Images

More recently, the EU introduced the so-called Spitzenkandidat (lead-candidate) process. The Spitzenkandidat system was applied in 2014 and it saw Jean-Claude Juncker — the chosen candidate of the European People's Party (EPP) – become the president of the Commission. However, there is an ongoing debate in the EU as to whether this process should be applied this year.

Why is the vote important?

"The next European Parliament won't have a clear majority as a result of these elections," Alberto Alemanno, a European law professor at HEC University in Paris, told CNBC at an event in London in February. This suggests it will be more difficult to implement laws at the European level. Current opinion polls show that the two mainstream parties, the conservative EPP and the socialist party S&D (Progressive Alliance of Socialists and Democrats) will lose their majority. Up until now, when these two parties agreed on the direction of policymaking, they had enough seats combined to approve any legislation needed. But this could end with May's election, meaning they will need to form agreements with other parties.

"The real challenge will be to find compromises among more than two big mainstream groups," Florian Hense, a euro zone economist at Berenberg, told CNBC via email. However, he highlighted that despite the upcoming split in voting intentions, pro-European parties are likely to still have the biggest share in Parliament. "Opinion polls still suggest a two-thirds majority for the mainstream parties," he said. "(And) even if the radicals have big plans for the EU, they lack both democratic support and a common position to deliver them." However, not everyone shares this opinion. A report from the European Council on Foreign Affairs showed that anti-European parties are on course to win a third of the seats and would "frustrate activity, undermine the security and defense of Europe, and ultimately sow discord that could destroy the EU over time." The same think tank said that anti-European parties are likely to work together to undermine European cooperation, such as pushing for an end to sanctions on Russia. "Overall there will be more political volatility and this will inevitably affect the quasi-automatic adoption of European Commission proposals," Alemanno said.

Generally speaking, the European Commission is in charge of proposing laws, which are then discussed and approved by every country's minister at European Council meetings. The European Parliament then votes on these proposals. According to Alemanno, 95 percent of European Commission proposals are adopted by the European Parliament and the Council. Significantly more than the percentage passed by U.S. lawmakers, he added. "We are going to witness a sort of Americanization of the European decision-making progress by having a less automatic adoption of proposals," Alemanno said.

Who are the winners and losers?

The center-left is likely to be the biggest loser. This has been the case in the majority of national elections in recent years. Alemanno explained that this is the case because voters feel the center-left has not delivered on their core principles in the last few years, mainly on lowering inequality. Based on the projections seen above, center-left politicians are likely to lose around 6 percent of their current representation in the European Parliament, on a proportional basis.

President of European Commission Jean-Claude Juncker. Armend Nimani | AFP | Getty Images

Following the same principle, the center-right lawmakers are poised to lose about 2 percent of their current representation in Parliament. The biggest gains could be for right-wing and far-right parties, including the Europe of Nations and Freedom Group — of which Italy's anti-immigration Lega is currently part of.

Who are the big personalities?

There are a few names to bear in mind ahead of the vote. Matteo Salvini, the Italian deputy prime minister and head of the Lega party, is one of them. Salvini has been traveling to different European cities to gather support from other like-minded parties, including Poland's ruling Law and Justice Party, to form a nationalist movement at the European Parliament. Salvini, who has seen surging popular support since getting into power, is reportedly considering calling a snap election in case his party polls well in the EU elections. France's Marine Le Pen, leader of the far-right party The National Rally, formerly known as National Front, is hoping to translate the current public uproar in France to votes at the EU elections. She is not running in the election herself, as she wants to keep her job at the French Parliament. She appointed 23-year-old Jordan Bardella as the party's leading candidate.

What are the top jobs up for grabs?

The European elections will open up a number of jobs at the EU's highest level. There will be a new European Parliament president; a new European Commission president as well as a new head of the European Council. The top vacancies are likely to be spread across European countries. This is then likely to influence the appointment of the new president of the European Central Bank, with Mario Draghi ending his mandate in October.

What are market players looking at?

In the minds of investors, there are two key questions: How much political volatility there will be; and who'll take the top jobs? They want to understand how much and what kind of legislation will be put forward in the new political cycle. But perhaps, and even more importantly, there is a strong interest on what will happen to monetary policy with the new ECB president. A new president may have a more hawkish stance compared to Draghi, which could mean higher rates in the euro zone. European leaders will have an initial discussion about the distribution of roles on May 28, and a final decision could be announced on June 21.