Taylor traveled to Rome to film Cleopatra.

In 1961, Taylor began filming Cleopatra in Italy. She played the title role, opposite Richard Burton, who played Mark Antony. At the time, Taylor was married to her fourth husband Eddie Fisher—a relationship that also began with an affair as he was married to Debbie Reynolds at the time—and Burton was married to his first wife, Sybil Williams.

The co-stars started a love affair.

While filming the movie—which took two-and-a-half years altogether—Taylor and Burton embarked on a tumultuous affair. According to Entertainment Weekly, they would stay in their trailers together when they were supposed to be on set, and the cast and crew were witness to both their good times and their epic fights. When Fisher left Rome, where he was staying with Taylor, it was considered confirmation of the infidelity.

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The scandal was international news.

Two movie stars falling in love on the set of their film and breaking up both of their marriages in the process was (and still would be) a major celebrity story. Paparazzi are said to have snuck onto the set by pretending to be extras. According to Biography, when astronaut John Glenn orbited the Earth in 1962, some newspapers featured Taylor and Burton on their front pages instead.

One newspaper that definitely did not approve of the couple was that of the Vatican. The city's paper condemned the affair, calling it "erotic vagrancy."

Per EW, this wasn't the only public disapproval Burton and Taylor faced. A Georgia congressperson asked the attorney general not to allow them into the U.S. due to "undesirability."

Burton and Taylor eventually made it official—twice.

Despite its dramatic start—and middle and end, for that matter—Burton and Taylor were together for years. They got married in 1964 after their divorces were finalized and remained married for 10 years. After getting divorced in 1974, they remarried in 1975, only to split up again a year later. During their marriage, Burton adopted Taylor's child, Liza Todd, who she had welcomed with her late second husband Mike Todd, and the couple also adopted their daughter Maria Burton together.

The pair also worked together again and again. Including Cleopatra, they made 11 movies together, including Who's Afraid of Virginia Woolf? and The Sandpiper.

Taylor had no regrets about their relationship.

In her 1987 book Elizabeth Takes Off, Taylor, who died in 2011, wrote about her relationship with Burton and the love she continued to feel for him years later. (Burton had died three years before the book's publication in 1984.)

"Despite what the press wrote at the beginning of our affair, I never regretted a moment of it," Taylor wrote (via People). "I believe in taking life in both hands and squeezing the most out of it ... I’ve always admitted that I’m ruled by my passions, and I can’t pretend I didn’t know what I was doing when I became involved with Richard. In fact, I thought about it plenty, and it sure was news."

She continued, "Richard and I lived life to the fullest, but we also paid our dues. Cleopatra was just the beginning and it was not easy for either of us, knowing we were hurting so many people we cared about. In the end our attraction was so powerful we were unable even to try and stop it."