During eight months of hearings Lord Leveson heard from some witnesses  - like ex-motorsport head Max Mosley - who called for new laws to set up a tribunal which would control the press.
Others, like Private Eye editor Ian Hislop, argued against statutory legislation, saying it would compromise Britain's free press.
BBC News asked a selection of Leveson witnesses, and other interested parties, what they wanted out of Lord Leveson's report.
The Leveson Inquiry has heard appalling evidence of press malpractice, abuse and criminality. It must have shocked the chairman as it did everyone watching. So I am optimistic he will put forward recommendations to ensure this stops.
Surprisingly, given what has happened, we already have quite good press laws and the laws are backed by a code. The problem is you can't go to law unless you are rich, and several national newspapers simply ignore their own code.
My hope is that Lord Justice Leveson will recommend that the power to enforce the law and the industry's own code be given to an entirely independent tribunal to which everyone has access irrespective of their means. This would require a statute.
It will not have escaped him that the newspaper industry, prompted by three Royal Commissions and several judicial inquiries, has promised on at least five occasions in the last 60 years to put its house in order. It has never kept its word.
So I hope he flatly rejects the Hunt/Black proposal for no statute and a mere contract between the newspapers.
It amounts to "trust us - we're journalists". Given the industry's record, this is, well, laughable.
British journalism has been poisoned in recent years by something that happened at most of our national newspapers. They became unaccountable, and then they became arrogant and cruel. An editor at the News of the World summed up the attitude. 'This is what we do,' he said. 'We go out and destroy other people's lives.'
That's not what most journalists think, but nor, sadly, has it been the view of a tiny minority. Almost every national newspaper participated in the attempt to destroy the lives of Gerry and Kate McCann. Eight newspapers tried to destroy the life of Christopher Jefferies, the Bristol teacher wrongly accused of murder.
This is bad for a profession whose mission, I was taught as a young reporter, is to bear witness to the world in a truthful way.
I want a body capable of asking the hard questions, pointing the finger of blame and ensuring that lessons are learned. It must be independent of the industry and of government and it should have the clout to ensure that mighty news organisations take heed.
Nobody at the Leveson Inquiry suggested that the judge should gag papers. They did ask, however, that stories should be properly researched and checked, that they should be fair, and that, if they risk harming anyone, they should pass a basic public interest test. I don't think any ethical journalist would want anything different.
There has been one central issue at the heart of the Leveson Inquiry. Is the press to remain free though operating within a tough, independent, entirely new system of self regulation? Or is it - for the first time since 1695 - to be subjected to Government controls and a system of state licensing which would be essential to make it work?
That choice is clear. There are no middle ways. "Statutory underpinning", or even "dabs of statute", are mere terms of art. They are state control under fragrant names.
I very much hope - along, according to opinion polls, with the clear majority of the public who do not want to see any additional legal burdens on the press - that Leveson will back proposals for a new, effective regulator which will, for the first time ever, have real powers of investigation and sanction, including the ability to fine newspapers up to £1m.
Such a system will both protect the public from media intrusion - dealing with the unacceptable practices we heard about at the Inquiry - and crucially protect the public's right to know.
The alternative of state intervention is abhorrent in a free society. It would mean the state controlling the regulation of those who are there to scrutinise them on behalf of the public. The consequences of that for our democracy would be incalculable.
I want Lord Justice Leveson to get out of the affairs of a supposedly free press, and take his celebrity and political cheerleaders with him.
As a defender of press freedom with no "buts", I cannot support any of the proposals discussed around Leveson.
"Statutory-backing" of a new regulator is simply state intervention by any other name. And  the alternative proposals put forward by Lords Hunt and Black, for an independent regulator with more powers to police and punish the press than are currently enjoyed by the police, make too many concessions.
• Writer and journalist
• Editor-at-large of Spiked Online, which says it "stands for liberty, enlightenment, experimentation and excellence"
• Formerly editor of LM, left-wing magazine which closed down after being sued by ITN for libel
• Author of book There is No Such Thing As a Free Press
The danger now is not crude censorship, but that an atmosphere is created in which we are left with a more sanitised, timid and tame press.
Press freedom, like all liberties, is indivisible. We either have it for all, or for none at all. And nobody has to pass an ethical test, or be as pious as Hugh Grant and Steve Coogan, to qualify for the right to freedom of expression.
Standing up for a free press means defending it for things we might not want to read or hear.
If the authorities must have a "statutory framework", let them look to the USA, where the First Amendment makes it illegal to pass any law "abridging the freedom of speech, or of the press", and where the notion of a Lord Justice proposing new press regulations would be laughed out of court.
We have sections of the press that don't inform the public, which seem to be aimed at providing little more than sensation and salacious forms of entertainment.  And when that involves harm to other  people, it is striking that no-one accepts responsibility.
I was struck that, when I sued and won damages from eight national  newspapers for defamation, no disciplinary action was ever taken against  the journalists associated with libellous articles.
Under the current system, the Press Complaints Commission has been unable  to reign in the excesses of certain sections of the press, and it  stretches credulity that one more attempt at self-regulation will result in something different.
There needs to be a regulatory body, independent of government and of  the press it regulates.
Unlike the PCC, this new body should have  powers to initiate investigations, plus significant powers to discipline  newspapers that flout journalist standards and make guilty publications  compensate their victims.
It is doubly important to bring in reforms because the no-win-no-fee system under which  I was able to sue has been abolished. If those rules had been brought before I was libelled, I would not have been able to get  justice.
Lord Justice Leveson repeatedly asserted his concern to maintain the freedom of the press. I therefore hope and expect his report will be based on common sense.
That means it must consider all of the evidence given to the inquiry in writing, as well as verbally in the selective and self-interested testimony of some celebrities and academics and the shocking but thankfully unusual experience of ordinary people who became embroiled in extraordinary events.
There was evidence of wrongdoing but there could be no real inquiry into phone hacking because of ongoing police activity. Neither was there much evidence heard of the millions of stories published each year that cause no offence or complaint. Indeed quite the opposite. They help ordinary people who are downtrodden by bureaucracy or subject to injustice. That is why the newspapers that are most often criticised are bought by so many.
They do not want any kind of state intervention or reduction in the power of the press to probe and expose wrong-doing or hypocrisy,  launch campaigns and indeed inspire, amuse and entertain.
Lord Justice Leveson also said he did not want his report to gather dust.
That means it must be capable of being embraced by the industry that has already shown its determination to put its house in order. Only the industry itself can change the culture, ethics and behaviour of the press.
The government and various lobby groups have seen the Leveson Inquiry as an opportunity to maybe get hold of the media and shape it, so it suits them.
That would be  a dreadful outcome - that would be like going back to Stalinism, and China and North Korea.
The great strength of this country  is that we do have a free press, and we have enough laws already to deal with the illegal activities the inquiry investigated.
So we don't need any more legislation and Parliament must not be allowed - in any way - to take control of the media.
However, we do need a genuinely independent regulator, able to control newspapers when they cross the line and stray into that grey area of smear and innuendo.
The regulator should be genuinely independent of the government and the media, and have the power to both hear complaints from ordinary members of the public and act on those complaints effectively by disciplining newspapers if they transgress.
A good model for the regulator might be the Independent Police Complaints Commission which works very well.
Lord Leveson's exhaustive inquiry into the media is due to report on Thursday with recommendations on the future regulation of the press and conduct between the press, politicians and police.