Are you baffled by the disagreements between the EU states, why the budget talks failed and what that means for the future of Europe?
Paul Reynolds, BBC News World Affairs correspondent, Emma Jane Kirby, BBC Europe correspondent and Guto Harri, BBC political correspondent, have been answering a selection of your questions to clear up the confusion.
What is the basis for calculating the EU contributions?
Russell, France (ex UK)
Contributions to the EU budget (called in the jargon the EU's "own resources") come from three sources.
The first is money collected from goods and produce coming into the EU - customs duties and agricultural levies. The second is an amount of VAT from each member state at an agreed rate. The third is an amount based on each member's gross national income.
The last is the largest, making up about 60% of the total.
Of course, the money contributed to the EU is then paid back to member states in the form of farm subsidies, regional and social payments, but this is not spread evenly.
What is this rebate that Britain thinks it is entitled to?
Toria Buzza, London, UK
The British rebate is money given back to the UK because it pays in far more to the EU budget than it gets back.
Britain gets back two-thirds of the difference between the two. It was agreed in 1984 at a summit in Fontainebleau and will need unanimity to get it changed.
Britain is the only country which has a rebate, but Germany, the Netherlands, Sweden and Austria - which also pay in more than they get back - pay less towards the rebate than some other countries.
The European Commission has suggested a general system under which all imbalances, as they are called, are adjusted according to a formula.
Can anyone be declared as the "winner" of last week's summit
Nobody was a winner among those who support a strong EU.
The French and British had a row, as is often the case, but there was no agreement and agreement is what governments really want.
Those who oppose the EU are on the other hand delighted. They feel it is showing its weakness.
Do the general public in other EU countries really see the UK as the main culprit? Do we have any allies?
Caroline Reeves, Wiltshire
As far as the British rebate goes, Britain stood pretty much alone at the EU summit. Its 24 other EU partners believe the refund is no longer justified since Britain is now the third richest country in the Union and no longer deserves a generous payback.
But when Tony Blair suggested he would re-negotiate the rebate if the entire budget was overhauled, he did win sympathy from some member states, Sweden for example.
Like Mr Blair, these countries believe the EU should stop spending so much money to shore up agriculture and instead should be investing in 21st Century pursuits like technology and research to try to kick start Europe's sluggish economy into becoming much more competitive.
Germany backed France in arguing that a deal on farm subsidies had been sewn up in 2002 and therefore was not up for renegotiation. However, the conservative German Christian Democrat leader Angela Merkel, who is tipped to win an election expected in September, said that Chancellor Schroeder was wrong to attack the British rebate without attacking agriculture subsidies which largely benefit French farmers.
So Britain does have allies with its "less subsidies, less regulation" vision of Europe's future - but it is in stark contrast to the more protectionist, more closely politically integrated future that France sees for Europe.
Tony Blair does not like the proposed budget. What sort of budget priorities would he like to see adopted? Has he defined his budget objectives?
Ron Dyce, Hungary
Mr Blair actually accepted in an earlier negotiation holding steady the level of farm spending up to 2013.
That is why the French will not re-open the talks. However, Mr Blair has always argued that this agreement set ceilings not floors on farm spending and that further cuts should be made.
Instead, he says, money should go on research and policies for the future. This is easier said than done and will take some years to achieve.
How are payments from the Common Agricultural Fund decided?
Jeremy Willoughby, Newcastle, UK
Farm payments are decided by policies agreed by agriculture ministers from all member states.
Those countries with more farmers will get more payments.
France has a lot of farmers and gets a lot of such payments. Britain has fewer and therefore gets fewer payments. That is what has created the imbalances.
What is the logic behind Jacques Chirac's apparent proposition that Britain should forego its rebate without the Common Agricultural Policy being adjusted to correct the imbalance that underpins the rebate?
Stephen, Ipswich Suffolk
Jacques Chirac's logic is that the CAP is not imbalanced and therefore does not have to be corrected.
He argues that the CAP has changed over recent years and no longer pays farmers to produce so much food.
It is therefore said to meet the needs of maintaining food production and looking after the countryside.
As for the rebate, the French logic is that even if Britain is entitled to something back, it gets too much back. France actually contributes the most to the British rebate.
Why can't the UK just leave the EU? Would anybody in Europe care?
NV, Paris, France
Tony Blair insists that he is still a committed European and he does not want Britain to leave the European Union.
It is doubtful whether other countries, even those like France and Germany which blame the UK for "selfishly sabotaging" the budget talks by refusing to give up its controversial rebate, really want the UK to leave the EU either.
France, in particular, wants the EU to be a major world power, and sees the UK as a key partner in shaping a common foreign and security policy.
There are also other countries - the Nordic countries and some of the new members from Central Europe - which share either Britain's Atlanticist outlook, or its commitment to a liberal economy, or both.
Ironically, even if Britain wanted to leave the EU, it would have a hard job doing so. Unless the Constitution is approved, there is no formula or mechanism in place which allows a country to withdraw its membership.
If France, and Britain continue to veto changes to the rebate and the CAP, what would be the position of countries' net contributions in, say, five years' time?
David Jones, Aldershot, England
The European Commission says that between 2008-13, if the same system is used, the average net contributions would range from 0.56% of gross national income (GNI) for the Netherlands to 0.54% for Germany, 0.41% for Italy, 0.38% for Austria, 0.37% for France and Cyprus, 0.31% for Denmark and 0.25% for the UK and Finland.
You can see why the UK likes the rebate. Without it, it would be the biggest net payer at 0.62% of GNI.
What, in a nutshell, does the constitution say and why don't the Dutch like it?
Catherine Prisk, London, UK
The constitution starts by defining the areas in which the EU can operate and those which are left to national governments.
It then makes EU action in some of those areas easier by having more majority voting.
However it allows member states to have the final say in the key areas of tax, foreign policy and defence.
Dutch voters gave many reasons for voting against the constitution. Many felt the EU was going too far too fast, and that they had no say in the matter.
Recent events have shown that the EU needs time to digest its 10 new members. Is it wise or feasible to consider postponing the accession of Romania and Bulgaria?
François Crabbe, Belgian citizen, Phnom Penh, Cambodia
The accession treaty with Bulgaria and Romania was signed earlier this year, so it would be difficult for EU states to go back on the decision to admit them.
However, the treaty has to be ratified, and the ratification is carried out by parliaments rather than by governments.
If any national parliament votes against ratification, then the deal will be off.
Even under the existing agreements, there is some flexibility over the timing. If the countries are not ready to join in 2007, this can be put back to 2008.
The bigger question hangs over Turkey. Negotiations about its terms of entry are due to begin in October but it could be many years before there is a result.
Is it likely that the EU will be downsized?
Steve Richards, Wimborne, UK
If by downsized you mean reduced in numbers, the answer is No. In fact, other countries want to join.
If you mean reduced in responsibilities, this is one possible outcome of the debate triggered by the failure of the constitution, though perhaps not the most likely.
Some want the EU to have more power and the constitutional treaty set out new areas in which it could act - justice and home affairs for example.
Others want it to go no further and some want to give some powers back to member states. There is currently no agreement on what to do.
What is in store for Europe in the next few years? Is the EU going to grow, or are we seeing it wane?
Karen, Edmonton, Canada
The EU is in a fair amount of chaos at the moment and until it sorts itself out, its political and diplomatic influence in the world will be weakened.
It is not a counterbalance to the US. However, economically it is still very powerful as one of its rules is that it acts as a bloc in world trade negotiations and it has some very powerful economies within it.
Europe will probably going on doing what it has often done - taking one step forward and two back, or vice versa.