Many expected Democrat Joe Biden to win by a landslide, but the vote dragged on for five days before a winner was declared - and it was so close in many states, the current leader is refusing to concede until all legal matters surrounding the balloting have been completed.
President Trump has even suggested the contest was rigged in an attempt to unseat him.
May has taken to social media to share his thoughts about the election, confessing, "I've spent a lot of time in the States, so I have a little bit of understanding - not enough understanding to make me even have a clue what happened in this recent election."
"It seems to me there are good people on both sides - this is indisputable. Between Republicans and Democrats, there's enormous polarization, and the country is split down the two, and not in a very amicable way. But there are definitely good people on both sides, and I don't think anyone can dispute that. And the other indisputable thing is there's a lot of skullduggery going on...
"To us over here (in the U.K.), almost to a man, we were shocked that almost half of America could look at what Donald Trump has done over the last four years and like it and actually want more of it. I mean, to us, it's almost impossible to understand that. And this is where you guys can start to hate me."
"But what I'm telling you is based on the information that we have been fed, that was an inescapable conclusion. It seemed, from the way it was painted and the media that we tune in to, that the man constantly lied and bullied and cheated and made a complete disgrace of himself. But still, 70 million people went, 'Okay, he's a good man'."