BBC Europe correspondent Matthew Price has been exploring the corridors of power in Brussels, and here he explains what each EU institution does. Come on a video tour with him.
There are 28 EU commissioners - one from each member state - and each one focuses on a policy area, for example justice and home affairs, or the EU internal market.
The Commission's job is to draft EU laws and act as "guardian of the treaties". It enforces EU rules, and if a member state delays enacting an agreed policy, or simply refuses to comply, then the Commission will warn them and if necessary pursue them at the EU Court of Justice. The Commission can levy fines or suspend EU funding.
New EU laws, or revisions to existing ones, come about usually after requests from governments, Euro MPs or lobby groups. There is often pressure from all three areas for the Commission to take action.
The Commission has a staff of about 33,000. The new Commission President is former Luxembourg Prime Minister Jean-Claude Juncker.
Council of Ministers
Usually this institution is simply called "the Council". It represents the governments of the member states; the ministers meet regularly according to their policy area.
EU laws become part of national legislation after detailed negotiations between the Council and the European Parliament. They examine draft laws from the Commission and make recommendations, so the final text is a compromise - often the result of numerous amendments.
Voting in the Council is weighted according to a country's size and economic power, so for example Germany has a bigger weight than Luxembourg. It is called qualified majority voting (QMV). Germany, France, Italy and the UK have 29 votes each, while Malta has three.
But for taxation or foreign policy issues, such as trade agreements or sanctions, unanimity is required.
EU summits are meetings of a separate institution - the "European Council" - that is, when all the heads of government meet. It is their job to set the EU's main priorities and overall policy direction. Their chairman is European Council President Herman Van Rompuy, who took office in 2009 and will step down in December 2014.
The Lisbon Treaty, signed in 2007, gave the European Parliament more powers than it had previously.
It is the only directly elected EU institution, and Europe's biggest elections yet took place in May 2014.
The parliament has grown because 13 countries - mostly ex-communist states in Central and Eastern Europe - have joined since 2004.
There are 751 MEPs. Germany has the most - 96, France 74, the UK and Italy 73 each, and the three smallest countries - Estonia, Luxembourg and Malta - have six each.
A majority of MEPs want the parliament to be permanently based in Brussels, to stop the expensive monthly shuttle to Strasbourg, where the full "plenary" sessions are held. But France wants to keep the Strasbourg sessions and switching to a "single seat" in Brussels would require treaty change.
MEPs now have "co-decision" powers in nearly all policy areas, meaning that they shape EU laws on an equal basis with the Council. Before the Lisbon Treaty they had little influence over agriculture, fisheries or the EU budget.
European External Action Service
The EU's new diplomatic service was one of the key innovations under the Lisbon Treaty, intended to give the EU "one voice" internationally.
The EEAS is led by Baroness Ashton from the UK, a Labour Party peer, who will step down in December 2014.
In 2012 the budget for the service was 489m euros (£422m; $649m), and it has a staff of 3,500 (1,500 in HQ and 2,000 in delegations).
There is much dispute about whether the EEAS has made EU foreign policy any more coherent. A European Parliament report this year called the service top-heavy and slow to react to crises. But Catherine Ashton's office argues that the EEAS has responded efficiently to emergencies in Africa and has achieved successes elsewhere, such as the April 2013 Serbia-Kosovo deal, reached after long, gruelling talks.