Rupert Murdoch’s legacy as a media mogul will be tested on Tuesday when British regulators report to the government whether 21st Century Fox should be allowed to buy the rest of Sky, the British satellite giant.

Mr. Murdoch has long dreamed of adding Sky to his array of global media assets. His media conglomerate, 21st Century Fox, already owns a 39 percent stake in the British satellite provider that also has divisions in Italy, Germany and elsewhere in Europe, and had proposed taking over Sky in 2010, but that effort was abandoned amid a telephone hacking scandal.

As part of their review, British regulators are scrutinizing whether 21st Century Fox meets the country’s broadcasting standards and whether the 11.7 billion pound, or $14.9 billion, takeover would unfairly hamper the British media landscape. They are also evaluating whether 21st Century Fox executives are “fit and proper” to retain broadcasting licenses in the United Kingdom.

The details of the review are not expected to be made public on Tuesday.

The timing is awkward for Mr. Murdoch and other 21st Century Fox executives, including his sons, James and Lachlan. They have tried to put an end to a sexual harassment scandal at Fox News that led to the ouster of its top host, Bill O’Reilly, and a chairman, Roger Ailes, yet those issues have arisen in the British review.

It also is likely to renew criticism that Rupert Murdoch holds too much sway over the British media, which he has denied.

James Murdoch, chief executive of 21st Century Fox and the chairman of Sky, said last month that he was confident the proposed transaction would be completed by the end of the year.

Here’s what you need to know about the British review, and how it may affect the Murdochs and plans for 21st Century Fox.

What is the review about?

Two politically independent British regulators — the Office of Communications, or Ofcom, and the Competition and Markets Authority — were asked by the government to review 21st Century Fox’s proposed takeover of Sky soon after the deal was announced in December.

Much of the focus has centered on Ofcom’s investigation. It is looking at whether the takeover would limit the types of media access British consumers would have and whether 21st Century Fox executives meet the country’s broadcasting standards.

In a separate but connected review, the regulator also must determine if 21st Century Fox’s management, particularly James Murdoch, are “fit and proper” to retain Sky’s broadcasting licenses.

That last point represents a potential stumbling block for 21st Century Fox. When the company tried to acquire Sky in 2010, Ofcom criticized James Murdoch’s handling of a phone hacking scandal at The News of the World, a British newspaper — since shuttered — that was then part of News Corporation, a predecessor to 21st Century Fox. While the regulator said that James Murdoch’s actions “fell short,” he was cleared and Sky ultimately was deemed “fit and proper” in that review.

Now, 21st Century Fox is grappling with the aftermath of a sexual harassment scandal at Fox News. Regulators at Ofcom have met with lawyers who represented several of the accusers as well as one woman who made sexual harassment allegations against Mr. O’Reilly. These meetings have raised questions about whether Ofcom would take into account the allegations, and the company’s handling of them, in its judgment on whether the company passes the “fit and proper” test.

21st Century Fox has said in a statement about the scandal that it had taken “prompt and decisive action” and had overhauled the leadership and management at Fox News.

The review will be sent on Tuesday to Karen Bradley, the British culture minister, who will make the final decision on the sale.

Analysts say there are four potential outcomes.

Ofcom may give its unconditional backing to the takeover, or recommend that the government block the deal, both of which are considered unlikely. It could recommend that 21st Century Fox make concessions, such as guaranteeing the independence of Sky News, the British news organization owned by Sky. Or the authorities may call for a more in-depth review by Britain’s competition authority, extending the outcome until the autumn.

No matter what happens, it will probably be weeks, if not months, before a final decision is made.

Why does Rupert Murdoch want Sky?

Rupert Murdoch has long coveted total ownership of Sky, whose assets include broadband services, a Pan-European satellite television network and popular original broadcasting with rights to sporting events like the English Premier League.

He founded Sky in the early 1990s, helping to jump-start a satellite television revolution in Britain that quickly spread across Europe. The company is now one of the region’s largest private broadcasters.

Mr. Murdoch’s previous plans to buy the remaining stake in Sky that he did not already own were scuttled because of the hacking scandal, leading to a widespread reorganization that included splitting his media empire into a publishing business and an entertainment business.

The potential takeover of Sky would cement Mr. Murdoch’s position in the fast-changing media landscape, where Netflix and Amazon are offering consumers new forms of programming. Sky owns NowTV, a European rival to these streaming services, which could help 21st Century Fox to compete.

Has the British election had an impact?

When 21st Century Fox proposed in December its takeover of Sky, many opposition lawmakers — and even some from the governing Conservative Party — were vocally opposed to the deal.

That situation has become even more complicated following British elections this month that left Prime Minister Theresa May without a majority in Parliament.

Opposition politicians have argued that the deal would limit the country’s media landscape and that the Fox News scandal is evidence that the company does not pass Britain’s “fit and proper” test. 21st Century Fox denies both allegations.

But without a clear majority in Parliament, and with talks on Britain’s leaving the European Union putting severe strains on her government, Mrs. May and her ministers are under pressure to postpone a final decision on the takeover.

What’s at stake for 21st Century Fox?

A decision — however unlikely — that 21st Century Fox executives are unfit to hold Sky’s broadcasting license would be a major reputational blow for Mr. Murdoch and his sons.

The proposed takeover is also central to 21st Century Fox’s global ambition to become a crucial player in determining how people watch programming online. Consumers now watch videos and shows on their mobile devices, an area where Mr. Murdoch’s company is lagging some of its rivals.

Analysts say that Sky — which is highly profitable and has 22 million customers across Europe — can offer 21st Century Fox direct experience with consumers, both as a provider of television and broadband services and through NowTV, its streaming unit.

And while 21st Century Fox is primarily interested in Sky’s programming and internet assets, potential concessions required by the British officials to guarantee the independence of Sky News may also weaken Mr. Murdoch’s hold over much of the British media.