It certainly wasn't love at first sight. In fact, not so long ago they didn't like each other very much.

"I don't hate the man," Elon Musk tweeted in July 2022, "but it's time for Trump to hang up his hat & sail into the sunset."

The Tesla and Space X founder's comment was prompted by a profane Donald Trump insult - put simply, calling Mr Musk a liar. Trump accused Mr Musk of lying to him about who he voted for in the last presidential election.

"Elon is not going to buy Twitter," Trump crowed to a rally crowd in Alaska.

Mr Musk did, of course, buy Twitter several months later - and he went on to endorse Trump’s Republican arch-rival, Ron DeSantis. The Florida governor even launched his presidential campaign with a glitch-ridden chat on Twitter Spaces.

But over the last few months the relationship between Mr Musk and Trump has not just thawed – it has reached a positively warm and steady simmer.

On Monday, Trump returned to Twitter/X after a year-long hiatus, hours before he and Mr Musk were due to sit down for what many expect to be a convivial chat streamed on the platform.

Both men will be hoping the conversation reaches an audience beyond the hyperactive paid-for users who dominate X discussion these days – and that it will be free of the technical glitches that overshadowed Mr DeSantis's ill-fated campaign.

The relationship between the tech tycoon and the Republican nominee has been a while in the making.

Mr Musk, who became a US citizen in 2002, has said that he voted almost exclusively for Democrats for decades.

But he soured on President Biden over issues including unions – Mr Musk is opposed to efforts to organise his car workers – and over a snub. He was not invited to the 2021 White House electric vehicle summit, despite Tesla's status as one of the world's largest EV manufacturers.

Under the Biden administration, Mr Musk's companies also faced a number of federal investigations over employment practices, his takeover of Twitter and claims about Tesla's autopilot feature.

In November 2023 he told a New York Times interviewer that he would not vote for Mr Biden again, but stopped short of supporting Trump, saying: "This is definitely a difficult choice here."

Mr Musk lifted the ban on the former president's Twitter account after buying the company.

And perhaps more importantly, his tenure has seen him go ever deeper into concerns that dovetail neatly with Trump's campaign: government censorship and persecution, complaints about the media, opposition to immigration, and anger at "woke" ideas.

"He craves attention and is a political chameleon," said Ryan Broderick, who writes the internet culture newsletter Garbage Day.

Mr Broderick said Mr Musk's online posts shifted dramatically a few years ago.

"He was tweeting neoliberal, happy-go-lucky things, and pride flags and so on, until around 2018, and the change happened pretty drastically after that," he said.

Since taking over Twitter, Mr Musk increasingly has engaged in political controversies and has spread inflammatory - and sometimes just outright fake - news stories.

During recent rioting in the UK, he engaged in a tit-for-tat with Prime Minister Keir Starmer, claiming that "civil war is inevitable" and sharing a fake post about "detainment camps" on the Falkland Islands.

He also bought into Trump’s claims - unsupported by evidence - that election fraud is endemic in the US.

Research by the Center for Countering Digital Hate – an organisation that Mr Musk attempted to sue in a case that was thrown out earlier this year – noted that so far this year Mr Musk has tweeted false or misleading voting claims 50 times.

And he regularly interacts with fringe, far-right figures and pro-Trump accounts on his own platform, amplifying their reach.

At the same time, his Silicon Valley connections link him to Trump’s inner circle. Mr Musk was a member of the so-called PayPal mafia - stakeholders who made fortunes when the payment processor was bought for $1.5 billion and who later became prolific investors and corporate founders.

PayPal founder Peter Thiel is an influential Republican who later employed JD Vance at his venture capital firm, Mithril Capital Management, then bankrolled his Ohio Senate campaign with a $10m donation.

In March, Mr Musk met Trump at his Florida resort. A couple of months later, Mr Musk hosted an "anti-Biden" dinner party, where the guests included Mr Thiel and Rupert Murdoch, according to US news reports.

Mr Musk has donated money to both Democratic and Republican politicians in the past. But although he insists he is not donating directly to any presidential campaign, he recently co-founded a pro-Trump political action committee, America PAC.

Political action committees have the leeway to spend huge sums supporting candidates and causes - although Mr Musk has said reports that he will contribute $45m a month to the PAC are overblown.

Nevertheless, his support for Trump was fully ensured just minutes after last month’s assassination attempt on the former president, when he tweeted: "I fully endorse President Trump and hope for his rapid recovery."

Trump seems to have mended fences with Mr Musk. At a news conference on Thursday he said: "I respect Elon a lot. He respects me."

"Elon more than almost anybody I know… he loves this country, he loves the concept of this country, but like me, he says this country is in big trouble, it’s in tremendous danger," Trump said.

Mr Musk has become a hero to an online cohort of young, mostly male supporters who might align with Trump’s ideas but who are, according to reports, less reliable voters.

The Trump campaign appears to be making a play for that segment of the population.

For instance, the former president recently did an interview with "edgy" podcaster Adin Ross, who repeatedly was banned from the streaming site Twitch for violating the site's conduct policies.

"Donald Trump is scrambling because he's looking for a way to invigorate his campaign," Mr Broderick said. "He's a showman and he understands that Elon Musk has similar instincts."

But he questioned whether the pair would get along face-to-face.

"I assume they will talk at and around each other, and it will probably not make much sense," he said. "And maybe somebody will say something crazy."

The BBC contacted X and the Trump campaign for comment.

The interview is expected to appear online at 20:00 ET on Monday (01:00 BST) .