In his memoirs, writer and director Franco Zeffirelli said that making this movie was the most fun he had in his entire career.
Before playing Katherina, Dame Elizabeth Taylor had never performed William Shakespeare's works (unlike Richard Burton, who was an experienced Shakespearean 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 shoot. As she found her way into the role, and became more confident, she asked writer and 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.
Dame Elizabeth Taylor and Richard Burton co-produced this movie, putting $1 million of their own money into the production and waiving their combined $2 million plus salaries, taking a percentage of this movie's gross instead.
The previous movie version of The Taming of the Shrew (1929) featured Mary Pickford and Douglas Fairbanks who, like Dame Elizabeth Taylor and Richard Burton, were married at the time. Pickford's and Fairbanks' marriage, however, was quickly deteriorating, while Burton's and Taylor's would not end (the first time) for another seven years.
Franco Zeffirelli originally proposed this movie as a vehicle for Sophia Loren and Marcello Mastroianni.