Elizabeth Taylor and Richard Burton co-produced the film, putting $1 million of their own money into the production and waiving their combined $2 million+ salaries taking a percentage of the film's profits instead.
Franco Zeffirelli originally proposed this film as a vehicle for Sophia Loren and Marcello Mastroianni.
After Cleopatra had failed at the box office, nearly bankrupting 20th Century Fox, when director Franco Zeffirelli suggested casting Elizabeth Taylor and Richard Burton his this film, he was told it would never happen by Fox executives. However, Zeffirelli was persistent, and in the end, he was able to convince Fox that the couple still had box office potential. Ultimately, he was proved correct, as the film was a huge box office success.
Although the play was first performed in London in 1593, it was not published until 1623, a few years after Shakespeare's death.
Before playing Katherina, Elizabeth Taylor had never performed Shakespeare (unlike Richard Burton, who was an experienced Shakesperian and already played roles such as Hamlet, Iago, Edgar, Hotspur and Romeo on stage), and she was said to be very nervous prior to the beginning of the shot. As she found her way into the role, and became more confident, she asked director Franco Zeffirelli if she could shoot everything from the first day of shooting again, as she didn't think her performance was up to scratch. Zefferilli assured her it was, but she was persistent, and on the last day of principal photography, the entire first day was shot again.
In his memoirs, Franco Zeffirelli said that making this film was the most fun he had in his entire career.
The dress that Elizabeth Taylor wears during Kate's final monologue is inspired by the dress that the model wears in Lorenzo Lotto's painting, "Lucretia". Taylor even wears a similar coverciere (shawl-like partlet), and has a necklace tucked into her bodice, just like Lotto's Lucretia.
The previous film version of The Taming of the Shrew featured Mary Pickford and Douglas Fairbanks who, like Elizabeth Taylor and Richard Burton, were married at the time. Pickford's and Fairbanks's marriage, however, was quickly deteriorating, while Burton's and Taylor's would not end (the first time) for another seven years.