News of their relationship spurred plenty of memes as many were caught be surprise.
Grimes has also attended official events with Musk — like the Hyperloop Pod Competition in July.
In July, after it was revealed that Musk has made donations to Republican political committees, Grimes defended his choice.
After her tweets began to receive some backlash, she added that "there is no world in which i’m ok w republican donations.."
A few weeks ago, rapper Azealia Banks claimed to be at Elon Musk's house in Los Angeles during the weekend while he was "scrounging for investors" following his tweet about possibly taking Tesla private.
Banks posted on Instagram about the ordeal, saying "I waited around all weekend while grimes coddled her boyfriend." According to the rapper, she and Grimes had planned to collaborate on some upcoming music, so she had flown to where she was staying.
"They bring me out there on the premise that we would hang and make music," Banks said in an Instagram DM with Business Insider. "But his dumbass kept tweeting and tucked his dick in between his ass cheeks once shit hit the fan."
Musk denied he had ever met or communicated with Banks.
With increased scrutiny of Tesla's financial future coming from both the press and the SEC, Musk and Tesla have been busy detailing more information about the possible plan to take the company private. Musk recently gave a brutally honest interview with The New York Times, where he revealed that the "excruciating" last year of work had begun to impact his personal health.
Speaking with the Times, an emotional Musk "choked up" at points during the interview as he recounted what he called "the most difficult and painful year of my career." He also said he's been having trouble falling asleep.
But even more recently, Musk and Grimes have unfollowed each other on Instagram, and Musk unfollowed Grimes on Twitter, which has caused some to speculate that their relationship may be rocky at the moment.
The couple unfollowed each other on Instagram over the weekend, but Grimes still follows Musk on Twitter as of press time Monday, and neither has made any public statements about the status of their relationship.