The first European election since the enlargement of the European Union to 25 states took place on 10-13 June.
Some 350 million people had a chance to vote for the new 732-member parliament, making it the largest democratic election outside India.
BBC News Online answers some key questions about the vote.
The largest parliamentary groups are, as before, the Centre-Right group (the European People's Party - European Democrats, or EPP-ED) and the Socialist group (party of European Socialists).
They also have roughly the same share of seats as they did in the old parliament.
The parliament has grown, and sprouted 10 new flagpoles
The Liberals remain in third place, though they have increased their share of seats dramatically through an alliance with centrist groups from France and Italy.
The parliament's main Eurosceptic group has also increased in size and is likely to become more visible, though not necessarily any more influential.
Why was turnout only 45.7%?
Turnout fell below 50% in the 1999 European election, and fell again in 2004, but still has not reached the level of US mid-term elections (usually below 40%). At the first election to the European parliament, in 1979, turnout was 63%.
Provisional figures suggest that turnout in the 15 older EU countries was almost exactly the same in this election as in 1999. However, in the 10 new member states the average was a mere 27%.
Within the 15 older member states, turnout trends vary widely. Participation is highest where voting is compulsory (Belgium, Greece and Luxembourg) but is also traditionally high in Italy. Malta and Cyprus bucked the trend among new member states in 2004, with turnouts of 82% and 71% respectively.
MEPs sometimes argue that more people would vote if political parties, which are usually preoccupied with national politics, put more effort into their European election campaigns - and if national media took more interest in the EU.
Other commentators say the problem is that most voters have little love for European institutions, and little understanding of the way they work. A constitution agreed by member states in June 2004 is designed to simplify the EU and bring it closer to the people.
Will my vote change the EU's policy agenda?
Not much. It is the European Commission, not the parliament, that proposes all community legislation (though it often takes its cue from national governments, and sometimes from the European Parliament too).
A European election never has the power to change a government, unlike a national election, though the outcome in 2004 may have helped to ensure that the new president of the commission was from the centre-right (Portugal's Jose Manuel Durao Barroso, who will take office later this year).
Candidates for this post are chosen by the EU's national governments, but are approved by the parliament.
What difference will the election make to the rest of the world?
Again, not a huge amount, on the face of it. The European Commission and the Council of Ministers are more directly involved in international affairs than the parliament.
The parliament sometimes takes a stand on issues which affect the EU's relations with foreign countries, such as Washington's request for personal data on passengers flying to the US. MEPs have insisted that EU data protection rules must not be violated.
The parliament can also affect foreign industries that export to the EU. For example, the directive on animal testing of cosmetics applies to any product sold in the EU.
The parliament also has a say over the use of the EU foreign aid budget, which is the largest in the world - though it has no influence over the Common Agricultural Policy, which has a damaging effect on farmers in developing countries.
What does the European Parliament do?
The European Parliament has a big influence on the lives of citizens in EU member states, whether they realise it or not. EU laws apply in all member states, and most laws passed by national parliaments are drafted in response to European directives (framework laws that have to be transposed into national law within a certain timescale).
As the European Parliament has the power to amend or reject most proposed EU legislation, it is often argued that members of the assembly (MEPs) have more real power than members of national parliaments.
Can you give me some examples of EU laws?
Here are a few that have been amended or adopted since 1999:
- Working time directive. This introduces limits on the hours employees can be made to work, and regulates rest periods, annual leave and night work. From August 2004 it applies to junior doctors.
Cosmetics directive. This regulates what industry can do to test cosmetics on animals, and bans animal testing of cosmetics after 2009.
- Takeovers directive. This establishes standard EU rules on takeover bids, and restricts the tactics companies can use to avoid foreign takeovers.
- GM food regulation: This governs the amount of GM products allowed in food and the labelling required to alert the consumer.
How many MEPs does each country elect?
This varies according to the size of the country. Germany, the biggest country in the EU, has 99, while Malta, the smallest, has only five at present. Smaller countries generally have more seats per head of population: Luxembourg has one MEP per 76,000 people, whereas the UK has one MEP per 760,000 people.
Do MEPs represent their national party or a European party?
MEPs often represent both a national party (such as the German Christian Democratic Union or the French Socialist Party) and a European party (such as the European People's Party or the Party of European Socialists).
Some MEPs (such as British Conservatives) only belong to a national party - but even then, they are nearly always a member of one of the assembly's parliamentary groups. Groups vote as a united bloc when they can, and have whips whose job is to promote group discipline.
However, it is usually the national party which decides whether an MEP is selected to run again in the next election.