The play opens as the student Lucentio arrives in Padua. He hears that the merchant Baptista has two daughters, but the younger, prettier daughter, Bianca, cannot be married before her strong-willed sister, Katherina. On seeing Bianca, Lucentio falls in love with her and changes identities with his servant Tranio, so that Lucentio can pretend to be a teacher to Bianca, named Cambio, while Tranio, pretending to be Lucentio, can bid for Bianca's hand with her father, Baptista.
Bianca already has two suitors, but doesn’t like either. The elderly Gremio hires Lucentio, disguised as Cambio, the Latin tutor, to woo Bianca on his behalf, while the other suitor, Hortensio, disguises himself as a music teacher, named Licio, to get access to her. Meanwhile Petruchio, a young adventurer from Verona, arrives to visit his friend Hortensio. He learns about Katherina and decides to woo her, aided by both Gremio and Hortensio.
Baptista is enthusiastic about Petruchio’s suit because the feisty Katherina is a burden to him and is continually quarrelling with her sister and with him. Petruchio will not be put off as he woos Kate and he fixes their wedding day. At the church, where Kate unwillingly awaits him, Petruchio arrives in an absurd outfit and after the ceremony he leaves for Verona immediately, with his new wife.
Meanwhile, Tranio, disguised as Lucentio, has proven that's his mother is richer than Gremio, and Baptista has given permission for Lucentio to marry Bianca, as long as Lucentio's mother assures Baptista that she gives approval for the match. Tranio therefore tricks an unsuspecting traveler, the Pedant, into pretending that she is Lucentio's mother to give Baptista the needed assurance.
Kate, having reached Verona, is mistreated by Petruchio and his servants, and is denied food and sleep. To teach her to obey him, Petruchio does not allow her new clothes or a hat. Eventually, worn down by her husband’s relentless eccentricity, Kate submits and accepts all his eccentricities. They set off to visit her father in Padua.
On the journey the couple meet Vincentia, Lucentio’s real mother, who is subjected to a strange conversation as Petruchio tests Kate’s obedience. The three reach Padua where Baptista has been tricked into believing the Pedant is Lucentio’s rich mother. No one believes that Vincentia is Lucentio's real mother and she is about to be hauled away as a lunatic when Lucentio returns from a secret wedding with Bianca and unravels all the confusion and mistaken identities.
Baptista holds a wedding feast for both his daughters. Hortensio, rejected by Bianca, has married a widow. As the men relax after their meal Petruchio devises a competition to prove whose wife is the most obedient. Bianca and the widow fail to come to their husbands when called while Kate lectures the women on the duties of a wife.
