See the post below for a great table on the responses of the 3 big parties; victims and the press to the emerging proposals for a new regulator.
Here, I've copied in a point-by-point FAQ from The Guardian summing up many of the points you need to know to really grasp this thorny issue
Its also necessary to put this into wider historical context, something we'll look at in more detail
Is it statutory regulation, how would the new watchdog deal with phone hacking and what do victims of media intrusion think of it?
How will press regulation be different now from before?
Culture secretary Maria Miller has claimed the prospect of investigations, fines of up to £1m for the worst or serial offenders will make it one of the toughest regulators in the world. While the predecessor Press Complaints Commission had no powers to impose fines, it was its lack of independence from newspapers that caused its demise. Its inaction over allegations of widespread phone hacking at the News of the World led it to being branded a "toothless poodle". The new watchdog should be completely independent. The press will have no veto over who sits on the board and serving editors will not be members of any committee advising on complaints, unlike the old system in which editors adjudicated on each other.
Is it statutory regulation or not? (And what is statutory underpinning anyway?)
The new regulator will be established by royal charter, not law. The charter will be entrenched in statute so it cannot be changed by ministers. It could only be amended if there is a two-thirds majority vote in both houses of parliament. The wording, d
escribed by one observer as "artfully crafted" allows both sides to claim victory on the fundamental sticking point. David Cameron claims the deal rejects so-called "statutory underpinning" because there will be no law that mentions either the press or the new regulator. However, Labour, the Liberal Democrats and Hacked Off insist the clause means it is "underpinned by statute" and stops meddling by politicians.
Which publications will it affect?
Newspapers, magazines and news-related websites that choose to opt-in will be regulated by the new watchdog. The nature of the independent self-regulator means that membership is voluntary and some prominent publishers have vowed to oppose any body underpinned by statute. Fraser Nelson, the editor of the Spectator, said his magazine would refuse to pay fines imposed by an underpinned regulator. Downing Street said that "personal blogs" like the Guido Fawkes political website would not be covered, but news-related websites like Huffington Post UK would.
Who chooses the regulators?
The regulators will be chosen by an appointments panel set up in accordance with civil service rules. Some sections of the newspaper industry wanted a veto on who sat on the board and the Tories initially had some sympathy with their view. However they lost the battle. The appointments panel will have a majority of members who are independent from the press but one person "with a current understanding and experience of the press" and one serving editor will be on the panel.
Who will pay for it all?
The newspaper industry including regional newspapers and magazine publishers will pay for the regulator. Fines imposed on publishers will be reinvested in the arbitration unit which will be set up to adjudicate on smaller claims of libel and breaches of privacy.
Will the British press now be the most regulated in the developed world as some claim?
Hardly. The most plausible comparison is with Ireland's Press Council, which is recognised in statute but was not established by statute. Like the British model, the Irish Press Council was set up after negotiation between political parties and the industry. However, one key point of difference is that Ireland's Defamation Act 2009, which recognises the Press Council, gives the Minister of Justice the authority to decide [who] is fit to [sit] on the Council body. Political involvement in the British model can only be achieved with a two-thirds majority vote in both houses of Parliament. It did not go unmentioned that, on the same day the royal charter was unveiled in London, journalists in Burma managed to head off plans to lock many of the country's old restrictions back in place. The UK is 29th on the world press freedom index compiled by Reporters Without Borders, behind Denmark and Hungary, which both operate a form of statutory regulation.
What would the new watchdog have done about some of the practices described in Leveson inquiry?
The Press Complaints Commission's critical failure was its inability to intervene while several newspapers published seriously defamatory stories about the parents to Madeleine McCann. David Cameron wanted the reconstituted watchdog to have the ability to proactively investigate concerns and order £1m fines for systemic breaches. In the case of the McCanns, the fines would prove much greater than the libel damages they received through the high court in 2008 (the largest being £550,000 from Richard Desmond's company that publishes the Daily Express and Daily Star). The new regulatory body will also be able to direct apologies from newspapers and not simply require them. This raises the prospect of newspapers running front-page apologies and corrections if the breach is sufficiently serious.
What role did Hacked Off have?
It is understood that Hacked Off had four members at the all-night talks, including co-founders Brian Cathcart and Evan Harris, Martin Moore and Hugh Tomlinson QC.
What do the victims of media intrusion think of it?
Victims broadly welcomed the deal. They believe the royal charter will ensure the regulator is sufficiently independent of the industry and incorporate many of Leveson's key recommendations. Several victims said the deal brings to an end four months of political stalemate and, they hope, draws a line under the worst abuses of the past. "What we have got is a very good opportunity for at last a new regulator, independent of the corporate end of media control and independent of political intervention," said Professor John Tulloch, the 7/7 victim whose phone was hacked by the News of the World.
Who will be able to make complaints to the new watchdog?
As of Monday afternoon, it was unclear whether the new watchdog will allow group complaints – for example, from bodies representing the trans community or gay rights campaigners – but it is thought likely that it will. The current Press Complaints Commission does allow complaints brought by interest groups. Some newspaper editors have cautioned against the new proposals over fears it will lead to the watchdog being endlessly bombarded by lobby groups. The Tories wanted to allow group complaints where there was a "substantial" public interest. Labour and the Lib Dems, on the other hand, lowered the barrier, removing "substantial" from the test.
Who will face exemplary damages?
Newspapers, magazines or news-related websites that that decline to join the new regulator face having to pay exemplary damages in civil lawsuits. The clause is meant as a "carrot-and-stick" incentive to encourage wide industry participation – but is likely to face a legal challenge as opinion commissioned by the newspaper industry described it as incompatible with European Convention on Human Rights.
• This article was amended on 19 March 2013 to make clear that the PCC does allow complaints brought by interest groups