The convention will decide which direction the EU will take
Click here to watch convention chairman Valery Giscard d'Estaing talk to the BBC's Janet Barrie
Over the next year, the delegates are supposed to develop proposals to help the union become more democratic and more efficient before it expands to as many as 25 states by the middle of 2004.
One of their key challenges is to persuade Europe's citizens that the EU is not only a transparent organisation, but one which is relevant to their daily lives.
Distribution of power
European leaders agreed at a summit in Laeken last December to set up the convention, partly to avoid the drawn-out debates that accompany every attempt to amend aspects of the club's core treaties.
Convention issues:
Click here for your guide to the EU It will examine which powers and responsibilities should be concentrated in Brussels and which should be given to the member states.
These issues will include debate on whether the bloc should develop a comprehensive foreign policy or a harmonised taxation policy.
Final decisions will be made by government leaders, but the BBC's Chris Morris in Brussels says there is a real possibility that this next stage of reforming EU treaties could produce a draft of a constitution.
In his own inaugural address, former French President and convention chairman Valery Giscard d'Estaing declared that his forum would at least "open the way" to such a document.
The convention is due to meet around 20 times over the coming year.
The forum is also due to hear the opinions of "civil society": trade unions, business groups and non-governmental organisations will be invited to attend the sessions.
Wage war
But before it has even started work, the body has caused controversy.
The chairman, former French President, Valery Giscard d'Estaing, was appointed to the post amid much bickering after the country's incumbent president Jacques Chirac threatened to veto any other choices.
Critics of Mr Giscard d'Estaing feel that a 76-year-old former president is an inappropriate choice of candidate to bridge the gap between the EU and its people, and that the group as a whole features too many ageing politicians and not enough women.
Reports that Mr Giscard d'Estaing had demanded a hefty wage for the post, plus expenses and a lavish hotel room, did little to endear him to his opponents.
The European Commission says it wants the debate on Europe's future to be held in every town and village across the continent.
But other critics of the convention have denounced as undemocratic the fact that a 12-member presidium, and not the 105 convention delegates, will decide what reform options and issues will be put up for discussion.