In this time, it has moved from being a purely consultative body to a body whose assent is required in 90 per cent of EU-wide measures, from the Common Agricultural Policy (CAP), a farm-subsidy behemoth with a budget of 57 billion ($90 billion) a year, to joint technical standards. Its clout is reflected by the growing numbers of lobbyists who follow MEPs (Members of the European Parliament) at their base in Strasbourg and at sessions in Brussels and Luxembourg, a long-derided travelling circus that costs European taxpayers 180 million a year.
But the vast majority of European citizens are incapable of naming their local MEP and many, it would seem, could not care less. Participation this time may be even less than the record low turnout of 43 per cent in the last elections in 2009. According to a survey by VoteWatch Europe, the two main alliances of political parties that have ruled the roost for decades, the centre-right European People's Party and the Socialists, are neck-and-neck, each with a likely share of just over 200 seats. Next come the Liberals, expected to pick up around 75 seats, and the Greens, who could lose over 30 seats to leave them with about 35.
But the biggest beneficiaries will be among parties that are hostile to the EU or deeply suspicious of it. Far-right anti-EU MEPs in the so-called European Alliance for Freedom could pick up 39 seats. A more moderate bloc, the European Conservatives and Reformists, could get 43 seats. Meanwhile, far-left MEPs who deem the EU project has become a tool of unbridled capitalism could get more than 50 seats.
Two of the most closely watched performances will be those of the UK Independence Party (UKIP) and France's National Front (FN). Both have scored extraordinary gains in local elections, and if they outgun mainstream conservatives in the EU poll will consolidate their claims as players on the national stage.
The European Parliament has long had to fight a reputation for spendthrift ways and arrogant disconnection from the European public. But the criticism only really began to gain wider traction after the 2008-09 financial crisis, which exposed the faultlines in the governance of the euro single currency.
Today, the eurozone's macro-economy is improving. The euro is, for now, considered to be safe, Ireland and Portugal have exited bailout programmes and even Greece, a basket case, is doing better. But the public mood remains sour: budgets are tight, 26 million are out of work and in parts of the Mediterranean rim, youth unemployment is more than 50 per cent, breeding talk of a "lost generation that will never find full-time jobs.
Anti-EU sentiment thus brings together several strands, from British and Dutch conservatives who loathe what they see as a dilution of national identity by immigrants and Brussels' "meddling in national life, to French, Greek and Italian populists who say the EU is to blame for austerity.
Some analysts predict that, in the next parliament, the eurosceptic bloc is doomed to implode. Its parties have no common objective, are stridently nationalistic and are led by charismatic chiefs who do not like to share the limelight. As a minority they would have no legislative effect on the big EU projects such as the single market and the euro, say these voices.
But, said Nicolaus Heinen of Deutsche Bank Research in Frankfurt, this is not the point. European politics are played out in national capitals, he noted. Eurosceptic success would prompt policy shifts at national level, as governments respond to electoral pressure. They would become more hawkish on schemes led by the EU centre, including support for flagging economies, something that the financial markets would perceive as a potential risk for the euro.