A week into his reign, Musk has suggested banned accounts, including that of former US president Donald Trump, may be reinstated.
And on Friday, he oversaw a massive staff cull. There have been suggestions that as many as half of the company’s 7,500-strong global workforce will be cut as part of cost-saving measures, with Musk having tweeted “we need to pay the bills somehow”.
The controversial magnate also heads Tesla and SpaceX, and is one of the most famous - and notorious - figures in the world. But what do we know about his complex family life? Here, Yahoo News UK takes a look...
Musk has married - and divorced - three times.
His first marriage was to author Justine Wilson in 2000, ending in an acrimonious divorce in 2008. In an article for Marie Claire in 2010, she claimed: “Elon's judgement overruled mine, and he was constantly remarking on the ways he found me lacking.
"‘I am your wife,’ I told him repeatedly, ‘not your employee.’ ‘If you were my employee,’ he said just as often, ‘I would fire you.’”
He married English actor Talulah Riley in 2010, having proposed 10 days after they first met. They divorced in 2012 but remarried in 2013. They divorced - again - on an amicable basis in 2016.
Musk's main relationship since then has been with Canadian singer Grimes, real name Claire Boucher. They began dating in 2018 before splitting in 2021.
He was also in a brief relationship with Amber Heard until early 2018.
Musk has nine known children, five from his marriage to Wilson.
In June, one of those five children, an 18-year-old daughter, legally changed her name to dissassociate herself from him. Her new name was redacted on court documents, which provided no information about the nature of their relationship.
He has had two children with Grimes in the past two years. They are named X Æ A-Xii and Exa Dark Sideræl.
In July, it also came to light that Musk fathered twins with Shivon Zilis, an executive at his Neuralink company, in November last year.
Musk's parents - engineer Errol and dietitian and model Maye - divorced around the time he was 10 years old.
He has a strained relationship with his father, with Errol Musk saying in an interview in August that he isn't proud of his son. Musk has previously said his father is "a terrible human being".
He has a better relationship with his mother. Only on Monday were they appearing in fancy dress together at a Halloween party in New York City.
In August, Maye revealed she sleeps in Musk's garage when she comes to stay with him in Texas.
Musk has two younger siblings: 50-year-old Kimbal Musk and 48-year-old Tosca Musk.
Kimbal is also hugely wealthy, with Forbes estimating last year he has a net worth of $700m. A restauranteur and philanthropist, he went into business with Elon in the 1990s when they founded software company Zip2. It was sold to Compaq for $300m in 1999.
Tosca is a film-maker and director who runs the streaming production platform Passionflix. In an interview with The Times in July, she said it is wrong to assume she is extremely wealthy.
She said: "I don’t have tons of money. [Elon and I] are not the same person. Also it’s not like he’s cutting me cheques. We’re two different people.”
"I’m very frugal. I love a good coupon.”