The "Shrew" is Katherina Minola, the eldest daughter of Baptista Minola, a Lord in Padua. Her temper is extremely volatile and no man can control her. She ties her sister to a chair in one scene, and in another attacks a music tutor with his own fiddle. Her younger sister, Bianca Minola, is nubile and much sought after by the nobles. Baptista has sworn not to allow his younger daughter to marry before Katherina is wed. Bianca has several suitors, and two of them agree that they will work together to marry off Katherina so that they will be free to compete for Bianca. One suitor, Gremio, is old and grey, and the other one, Hortensio, is feisty and young.
The plot becomes considerably more complex when two strangers, Petruchio Guicciardini and Lucientio della Rovere, arrive in town. Luciento, the son of the great Vincentio of Pisa, falls in love with Bianca, while Petruchio seems interested only in money and fine jewels.
When Baptista mentions that Bianca needs a preceptor, both suitors compete to find one for her in order to curry Baptista's favor. Gremio comes across Lucentio, who pretends to be a man of letters in order to woo Bianca. Hortensio disguises himself as a musician and convinces Petruchio to present him to Baptista as a music tutor. Thus, Luciento and Hortensio, pretending to be teachers, woo Bianca behind her father's back.
Meanwhile, Petruchio is told by the suitors about the large dowry that would come with marrying Katherina. He attempts to woo the violent Katherina, calling her "Kate," quickly settles on the dowry, marries her and takes her home against her will. Once there, he begins his "taming" of his new wife - he keeps her from sleeping by blowing a trumpet, invents reasons why she cannot eat, and buys her beautiful clothes only to rip them up with a crudely forged bread knife. When Kate, profoundly shaken by her experiences, is told that they are to return to Padua for Bianca's wedding, she is only too happy to comply. By the time they arrive, Kate's taming is complete and she no longer wants to resist Petruchio. She demonstrates her complete subordination to his will by agreeing that she will regard the moon as the sun, and the sun as the moon.
Bianca is to be married to Lucentio (following an enigmatic subplot involving Lucentio's servant masquerading as his master during his stint as a tutor). Hortensio has married a chubby rich widow. During the banquet of cold meats, Petruchio brags that his wife, formerly untameable, is now completely obedient. Baptista, Hortensio, and Lucentio are incredulous and the latter two believe that their wives are more obedient. Petruchio proposes a wager in which each will send a servant to call for their wives, and whichever wife comes most obediently will have won the wager for her husband. Baptista, not believing that his shrewish Katherina has been tamed, offers an enormous second dowry in addition to the wager.
Kate is the only one who responds, winning for Petruchio a second dowry. At the end of the play, after the other two wives have been summoned also, Kate gives them a soundly-reasoned speech to the point that wives should always obey their husbands.