Here are the main findings:
The main finding of the report is that the current system of self-regulation, through the Press Complaints Commission, can no longer continue. Instead, the report calls for a new "truly independent" body.
This organisation should be free from government and industry influence. It would have powers to order newspapers to print corrections and could impose fines. It would be a voluntary system but one for which there would be incentives to join. These would include mitigation in future libel cases and a "kitemark". But it would have no power to stop the publication of any story. It also suggests the body should be able to carry out its own investigations.
Lord Justice Leveson describes legislation as "essential". This would recognise the independent regulator and its duties. This is similar to the system that has been introduced in the Republic of Ireland.
But some people, including the Conservatives, argue any legislation opens the door to the possibility of state control.
Lord Leveson said "the law should also place an explicit duty on the government to uphold and protect the freedom of the press".
The inquiry found the relationship between politicians and the media was too cosy.
It uncovered no evidence of deals between the Conservatives and Rupert Murdoch's News International, but it said the Prime Minister had gone to "great lengths" to woo the newspaper empire ahead of the last general election.
It said there was an immediate need for senior politicians to provide a "general estimate" of the volume of emails, phone calls, texts and letters they have had with media owners and executives. They should also set out a statement on their relationship with the media and publish details of meetings with media organisations quarterly.
the phone-hacking scandal triggered the resignation of the head of the Metropolitan Police and the most senior anti- terrorism officer in the UK.
The report is critical of the initial phone hacking investigations. But it found no evidence that failings were because of close links with the media. However, it does make a number of recommendations that could fundamentally change the relationship between the two. These include forcing all top-ranking police officers to reveal meetings with journalists and a ban on briefings being called "off the record". It also warns officers they should not drink alcohol when they meet reporters, but stops short of recommending a blanket ban. Use of the police national computer should also be restricted to stop leaks, and there should be a review of jobs senior officers can take in the 12 months after they quit the force.
Lord Justice Leveson warns the current system is broken, in part because victims of press abuses are not offered enough redress. He recommends a newly created regulatory body should be able to impose a series of sanctions. These should include fines of up to £1 million and the use of prominent apologies.
The report looked at The Sun's revelation that the son of the former Prime Minister suffers from cystic fibrosis.
Last year, Mr Brown suggested in the House of Commons that the tabloid had obtained the story by illegally hacking his medical records. This was denied but the report challenges the paper to explain more about its source. It also finds there was no "public interest in the story sufficient to publish without the consent of Mr and Mrs Brown".
The now-defunct tabloid had a "lack of respect", the report found. It highlighted the publication of Kate McCann's private diary and criticised the tabloid's lack of co-operation with the police investigation into phone hacking.
It said: "Most responsible corporate entities would be appalled that employees were or could be involved in the commission of crime in order to further their business. Not so at the News of the World. When police sought to execute a warrant, they were confronted and driven off by the staff at the newspaper."
At one point it seemed the inquiry could trigger the resignation of then culture secretary Jeremy Hunt. He was in charge of ruling on a bid by Rupert Murdoch to take over BSkyB, but faced accusations he had grown too close to the Murdoch empire amid revelations of matey text messages from lobbyist Fred Michel. The report found Mr Hunt had behaved properly, though it suggested he had perhaps to realise the full risk of "perceived bias". It was more damning of his former special adviser Adam Smith. It recommended the Government reconsiders how it judges if any one group has too much control over the UK media. The calculation include websites and the bar which "gives rise for concern" should be lowered.
While it says politicians should remain responsible for public interest decisions on media mergers, it recommends all lobbying on the issue should be recorded and published.