In a landmark speech UK Prime Minister David Cameron has said he wants the UK to have a referendum on a redefined relationship with the EU by 2018.
Mr Cameron warned that the EU must be more accountable to voters. His government is examining how to repatriate more powers from Brussels.
BBC News asked some prominent European politicians and analysts for their views on Mr Cameron's speech.
Elmar Brok, German conservative MEP
I agree with him that in Europe we need more democracy and more competitiveness. Therefore we need stronger European rules to get that.
I think a referendum in the UK would need a debate not just at the tabloid level. A debate about the pros and cons of membership can be helpful, to make clear what the EU means, and for sure also we have to change here. Yes, we can always look at Europe's competences. But we cannot allow cherry-picking in the internal market, because then we would have different levels of competitiveness.
He should also tell the British people what advantages the EU has for Britain. If for many years you always tell people how difficult, dangerous and expensive Europe is you cannot expect them to support it. You cannot do policy by saying that if the sun shines it is London or Berlin, and if it rains it is Brussels.
We can debate whether we can have less detailed legislation on certain questions. That's a good idea, but that's not a question of treaty change, it's a question of political will.
For sure the internal market is an important part of the EU. But it was the political goal from the very beginning to have closer co-operation within Europe to make peace possible. So it's not just the internal market. The vast majority of member countries will not follow the path of concentrating the EU just on that.
In 1908 Churchill as home secretary introduced the 48-hour working week in Britain, and now Mr Cameron is not accepting that at the European level. I think the internal market cannot be organised on the basis of destruction of social rights. We should work together to explain why we need Europe. I'd prefer Britain within the EU.
Euclid Tsakalotos, Greek left-wing Syriza MP
Since 2008, inside and outside the eurozone, opposition to austerity policies has been labelled populist, in a cynical exercise to conflate the popular with populism. But it is successive British leaders who have raised populism with respect to the EU to a fine art. The dream of a Europe as a vast "free" market with limited social rights, or "a more flexible, adaptable and open European Union", has been the goal. Hollowing out democracy has been the means.
David Cameron's reference to "the demonstrations on the streets of Athens, Madrid and Rome" is disingenuous.
Greater integration implies a willingness to share sovereignty; the central question is whether this will be accompanied by the creation of a European public space and new democratic institutions. The UK prime minister's understanding of the "national interest" and his opposition to a two-speed Europe has nothing to do such democratic accountability.
European peoples in the south can vote for any government they want - as long as the policies of austerity remain untouched; the same policies, that is, which have led to such a spectacular failure in the UK.
It is the opposition movements who are truly displaying "courage and conviction", but in order bring back an agenda of jobs, wages and pensions, and even more, to return some control over economic policy to ordinary people.
There is a democratic deficit within the EU. But David Cameron is on the side of those elites and financial markets that want to deepen that deficit still further.
Sampo Terho, nationalist True Finns MEP
I think the referendum promise was very welcome. I have high hopes that other countries will follow him and make similar plans.
But I also have a small concern that he wants to wait so many years before having it. I'm afraid Mr Cameron may be placing too much hope on the EU's will and ability to reform.
It's been a core ideology of the EU to advance towards a federal state and that means transferring more powers to Brussels. This may happen in small steps, but those steps have always been towards integration and regulation, done by Brussels. So this EU ideology is unlikely to change any time soon. I expect the EU to look very much the same in 2017 as it does now.
I share his view that the core idea of the EU should be free trade, and advancing trade relations. In Finnish discussions that was the main issue, and it still is. I'd like to see a referendum in Finland after the next EU elections [in 2014], because as I see it that's the last big chance the EU has for reform.
If we could see a landslide victory in Europe for parties that oppose the federal state then this would give huge momentum for significant reform in the EU.
It would be a significant change if the UK left, but not a blow or disaster. He's absolutely right that our main target should be to reform the EU so that it does not regulate so much. But I'm a bit sceptical that the EU has the will for such reform.
Finns are quite concerned about the development of the eurozone - more solidarity, common debt and all that. We want to remain an independent country.
Pervenche Beres, French Socialist MEP
Prime Minister Cameron delivered to the British people a self-interested speech, absolutely disconnected from European reality, and which has very little to do with the UK interest or with its commitment as a member of the Union since 1973.
Mr Cameron seems to forget that the EU is a union of freedom and a free market, not a union of markets or an open relationship.
By establishing a link between the results of the next general elections in 2015 and the potential organisation of an in/out referendum in 2017, he is trying to regain confidence among his own party, by arousing resentment against the EU in the British population.
The basis of the proposed referendum will be a future renegotiation of the relationship between the EU and the United Kingdom; does he really imagine that his country can have full access to the internal market without contributing to the European budget, and rejecting a common regulatory framework for the financial services which had a major responsibility for the current crisis?
We cannot afford this kind of "Europe on demand" project.
Mr Cameron is apparently convinced that the interests of his country would be better secured within an open and fully flexible European Union; this kind of semantics is closer to basic Thatcherism than to a real reflection on the future of the EU, and on the place and role the UK will have in future.
Marc Peeperkorn, correspondent for Netherlands daily de Volkskrant
"It is time to settle this question about Britain and Europe," concluded Mr Cameron in his long-awaited EU speech. He's right. Not only the discontent in the UK about the EU needs to be addressed, but also the frustration in the EU about the UK.
Four of the five principles of Mr Cameron's "new relationship" with the EU arouse little excitement. We all knew the UK sees the EU mainly as a single market which needs more competitiveness. Germany, France, the Netherlands, Finland, EU president Herman Van Rompuy, European Commission president Jose Manuel Barroso - they have been saying the same already for quite a few years.
Also, the principles of more democracy in the EU, more flexibility and regaining power from Brussels are debated over and over again among the member states. Not always with the full participation of London, by the way.
No, the real "news" in Mr Cameron's speech is that he wants to get rid of the "ever closer union" paragraph in the Treaty. That strikes at the political heart of the EU, because it was and is the justification (also in juridical terms) of EU legislation.
That, combined with his proposal for an in/out referendum, is potentially disrupting for the EU. Based on his speech today and actions in the last year, I think nevertheless Mr Cameron will defend any "new settlement" he negotiates with the other member states.
Jose Ignacio Torreblanca, Spanish political scientist
The best is no doubt the call for a cool-headed approach, a rational debate and the opening of negotiations with Britain's partners.
It's wise to first try and change the status quo and then submit the result to the public for its approval or rejection. That speaks well of British democracy and Mr Cameron's wish to reconcile Europe and the British public. But that's not enough.
Mr Cameron has squeezed himself into a very difficult situation. Ideally, he would want to transform the EU into something much better than what it is today: less rigid and bureaucratic, more competitive, democratic and open to the world. Should he bother to try and rally support for that vision, he could find many partners on the continent. But he does not lay out any convincing proposal on that matter, nor offer a roadmap for that process.
Having given up on improving the EU even without having tried, he goes for his second-best, i.e. to stay in the EU, albeit after having won some additional guarantees and exemptions from EU policies. But here numerous questions arise.
First, is there not a contradiction in his passion for the single market, which is basically about free and fair competition, and his wish to exempt the UK from EU labour regulations, which are a key part of every country's competitiveness?
The same with fisheries - is it just because British fishermen cannot compete with firms from other EU member states that he wants to repatriate fisheries policies, or is there a better argument? Could other member states also pick and choose which policies to repatriate?
Finally, why would the 26 fellow EU member states accept this? What would the UK give in return? Mr Cameron misses one key point: before he convinces the British public of the need to stay in the EU, he needs to convince the EU that it would be worse off without the UK.
Since he seems not to question that the UK would remain attached to the single market, even after formally leaving the EU, the truth is that his bargaining power is not great.
Jan Zahradil, Czech conservative MEP
I call it a breakthrough speech, not so much because of the referendum - I think that's just internal British - but because of the important vision of how the EU should be framed in future. He definitely opted for a flexible Europe, where states have the right to integrate according to their preferences.
Czech voters are not very enthusiastic about the EU, we can see it in all the public opinion research. I think also in other countries, where people are dissatisfied with the EU, Mr Cameron's speech could have an appeal - it presented an alternative vision to the Franco-German federalist paradigm.
On democratic accountability I think what he said is true. Even in the European Parliament we should represent something like pan-European interests, but we see every day that nothing like that exists. There is no European demos. In elections of all kinds, municipal or European, they vote according to national preferences.
The single market is a very crucial point - for us from Central and Eastern Europe the removal of trade barriers is crucial. It needs to be completed, as without it functioning there won't be any growth in Europe.
I was very glad that Mr Cameron did not refer only to the UK, but mentioned others. He seemed to want to open up these opportunities for other countries, if they wish to do so - a very statesman-like approach.
Despite the fact that most people here [in Brussels] are profound federalists, even they don't want the UK out of the EU. They should offer a certain space for negotiations. If they try to block it, and say no, they might push the British to say no to the EU. I don't think anyone wishes that to happen. I hope common sense prevails.
If the UK were to pull out the EU would be much weaker than before. Also, the UK would be able to survive without the EU, politically and economically, because it's a big power.