The European Union constitution is a rule book setting out what the EU can and cannot do.
It lays down the EU's values and political objectives and makes clear that member states confer powers on the EU, not the other way round.
It also opens the way to deeper EU integration, which some people argue will turn the Union into a superstate.
The constitution will become law only if it is ratified in every member state, in some cases by referendum.
The constitution takes several steps designed to reduce the risk of gridlock in the enlarged EU of 25 states.
It lowers the size of the majority needed for most decisions in the Council, and cuts the number of areas where a unanimous vote is required.
It creates a full-time president of the Council, who may give more continuity than the existing rotating presidency.
And it streamlines the European Commission, cutting one third of its members from 2014 onwards.
The constitution re-commits the EU to a common foreign policy and says it should develop a common defence policy.
It creates an EU foreign minister to co-ordinate diplomatic and foreign aid activities, and a diplomatic service.
But states must agree foreign policy unanimously. If they disagree, as over Iraq, the minister is powerless.
The constitution allows members to opt in or out of co-operation on defence. It also establishes an agency to co-ordinate arms procurement by EU states.
The EU constitution also:
Politicians sharply disagree about the constitution - about how much it changes, and whether it is good or bad.
Some see it as a missed opportunity to build a United States of Europe, while others complain it does precisely that.
Much depends on how it is implemented. For example, the European Council president could become a new force for EU integration - or just a figurehead.
Equally, the impact of the Charter of Fundamental Rights may hinge on rulings by the European Court of Justice.
The 25 EU member states were all meant to have ratified the constitution by the end of October 2006 - two years after they signed it.
Now that French voters have rejected it, the way forward is unclear.
The country could decide to hold a second vote. If it does not, the constitution cannot come into force in its present form.
If the text is altered, the ratification process will have to start again from scratch.