So, what happens now?
No state has left the European Union before. Up to the Lisbon Treaty, it did not even have rules that would allow it. However, Article 50 of that Treaty does make it possible, but the rules are brief and they are open to argument. Under them, departure occurs within two years. However, pro-Leavers want to delay pressing the button on the opening of Article 50 talks, so that departure could happen not in two years, but in four, or so - giving more time for negotiations to be completed on the UK's terms. Cameron's fellow EU leaders do not want to be drawn into months and years of haggling over Britain's status: "Out is out," the President of the European Commission, Jean-Claude Juncker said on Wednesday.
By contrast, the official Out campaign has said there is no need to trigger Article 50 until informal negotiations have taken place - potentially lasting years.
What to expect today
Martin Schulz, the President of the European Parliament, will hold crisis talks in Brussels at 8.30am, to agree a common position from MEPs. Despite the demands of UK pro-Leavers, they are expected to insist that Article 50 is triggered immediately, to prevent months of uncertainty.
Two hours later, Donald Tusk, president of the Council, Jean-Claude Juncker of the Commission, Mark Rutte, the Dutch prime ministers now in charge of the European Council's rotating presidency will meet Schulz and Jean-Claude Juncker. Expect a press conference in coming hours.
Mario Draghi, the president of the European Central Bank, has already made it clear that he will everything necessary to steady the stocks and financial markets. Global central bankers have promised to inject billions in liquidity.
Tomorrow, leading figures from the six founding member states - France, Germany, the Netherlands, Luxembourg, Italy and Belgium - will meet. The mini-summit was quietly organised a few weeks ago, but now the stakes have just risen incredibly.
David Cameron, if he is still in No. 10 Downing Street - and there are serious doubts that he can do so, but there is pressure on him to stay, too - will attend the European Council summit on Tuesday and Wednesday. Whatever the smiles in public, there will be fury directed towards him in private for creating the biggest crisis in decades - one that the European Union does not need right now, given every other pressure that it faces.
Enda Kenny will have to stand by Cameron, wherever he can. Ireland did not want the UK to leave. Now it must ensure that the UK gets the best deal it can, lest Ireland suffers, in turn. Sure, there are short-term advantages: Ireland will be more attractive to FDI investors. The country is the only native English-speaking country in the EU, with an Anglo-American attitude to corporation taxes and free trade. However, those very advantages will become harder to defend in a Union that will, in time, be without London. Ireland has often hidden behind the coat-tails of the British in late nights in Brussels talks. Now, Ireland may find itself more exposed than ever before.