The 751 newly elected Members of European Parliament (MEPs) will represent over 500 million people across the European Union (EU)'s 28 member states – and this scope gives rise to plenty of disagreements.
So what are the key issues facing the European Parliament?
Euroskepticism – or anti-EU sentiment – appears to have spread across Europe rapidly, fueled by anger at the euro zone crisis and the tough austerity measures introduced as a result.
Read MoreEuro zone economy loses steam as France lags
In these elections, the number of euroskeptic MEPs rose 19 percent to 143 seats, according to Sunday night projections. Anti-EU parties came first in France, the United Kingdom, Greece and Denmark, among other member states. The scale of the victory in France in particular came as a surprise, with more than 25 percent of the vote going to the Front National led by Marine Le Pen.
This rise in the number of anti-EU MEPs means that a large chunk of the European Parliament now actively wants its abolition.
"A polarized parliament is concerning because it doesn't offer what most voters want," Mats Persson, director of the Open Europe think tank, told CNBC.
"People generally want a middle way between 'no Europe' and 'all Europe'. They want less EU, but a better EU – and that choice is denied if it becomes polarized."
There could also be a market impact, according to Bank of America Merrill Lynch analysts Ruben Segura-Cayuela and Laurence Boone, who warned of an increase in fragmentation across European institutions.
"In our view, this situation may prevent further integration and, more importantly, provide no current clear sense of direction, which, in turn, may weaken economic policies and create further complications for financial market regulation," they wrote in a note.
But it's not all bad news, according to Persson, who argues there will be clear incentives for the pro-European MEPs to "huddle up and freeze out the anti-EU contingent."
"If anything, the European Parliament might become more integrationist than it currently is," he added.
2. Sluggish growth
Growth figures published earlier this month put paid to any notion that Europe's economic recovery was gaining any serious momentum.
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Across the EU, gross domestic product (GDP) rose by 0.3 percent during the first three months of the year, while the euro zone economy expanded by just 0.2 percent. Some Mediterranean countries performed especially badly, with a contraction in Italy, Cyprus and Portugal's economies.
"Last week's bleak first-quarter GDP figures have pulled the rug out from under the euro zone's so-called recovery," Nicholas Spiro, managing director of Spiro Sovereign Strategy, said in a note.
"The election is being held at a time when the euro zone is stumbling on the road to recovery, reform fatigue has set in (and) the governance of the bloc remains a shambles."