Before the play begins, a lord and his huntsmen discover Christopher Sly, a beggar, asleep and drunk. They play a trick on him when he wakes up by pretending that Sly is the lord and they are his servants. To help him recover from his "amnesia," they present the following play:
Baptista, a rich gentleman of Padua, has two daughters. The elder, Katherina or Kate, is so bad-tempered that she is known throughout Padua as Kate the Shrew (an Elizabethan word for an unpleasant woman). Baptista's younger daughter, Bianca, is gentle and sweet, and has two suitors, Hortensio and Gremio. However, Baptista won't let Bianca get married until someone agrees to marry Katherina first.
Two visitors to Padua arrive with their servants. The first, Lucentio, instantly falls in love with Bianca, and disguises himself as a teacher so he can see her more often. The second visitor, Petruchio, has come to Padua in search of a rich wife and hears that Kate is rich and pretty, but has an awful temper. Petruchio resolves to marry this famous wildcat and teach her how to be an agreeable wife. Baptista, with some misgivings, gives his permission.
Then follows the famous wooing scene. Whatever Katherina says, Petruchio is gentle with her and tells her he's determined they shall marry. They fight—she loudly and angrily, showing why she was called a shrew. He, on the other hand, praises her sweet and courteous words. At that point, Baptista arrives and Petruchio announces that he and Katherina are to be married Sunday.
On Sunday, Petruchio arrives late for the wedding, dressed like a clown, and behaves rudely in church. But the marriage is performed anyway. Then Petruchio refuses to stay for the wedding dinner and sets out for his house with Katherina.
They have an awful journey, with Petruchio behaving like a maniac. When the newlyweds arrive home, Petruchio is even stranger. He throws the dinner on the floor, pretending that the food is not good enough for Kate, and then dismantles the bed, saying it's a mess as well. In other words, he behaves just like Katherina used to.
The next day Petruchio behaves the same way, yelling at the servants and forbidding them to give his new wife anything to eat or let her rest. By this time, she is willing to be nice to her husband, because she is both very tired and very hungry. She also finds herself sticking up for the servants, when before her marriage she'd found fault with everything and everyone. Petruchio tempts her with some food but, since she isn't quick enough to say thank you, takes it away again.
He then decides to take her back for a visit to Baptista and orders a new gown for her. (Her old one had got spoiled on the journey.) Again Petruchio finds fault with it, and won't let Kate wear her new clothing, but says they'll travel in their old clothes.
Next Petruchio orders his horses be readied, saying it was only seven o'clock. Kate corrects him, saying it is noon. Petruchio replies: Are you still disagreeing with me? Until you agree, we're not leaving. Petruchio, you see, is trying to teach Kate that life is more comfortable if people agree with each other.
Finally they set out and have another disagreement Petruchio saying the moon is shining and Kate arguing it is the sun. He threatens to take her back to his house unless she agrees with him and Kate, weary of all this arguing, says he can call it the moon if he wants.
Petruchio has one last test for her: they meet an old man and Petruchio calls him a "fair maiden," looking at Kate. She agrees the old man is fair, and then Petruchio contradicts her again. So she changes her opinion to agree with him and they continue their journey.
When Petruchio and Kate arrive in Padua, they go to Baptista's to celebrate Bianca's marriage to Lucentio, and the marriage of one of Bianca's former suitors, Hortensio, to a rich widow.
Petruchio bets Lucentio and Hortensio that Kate is more agreeable than their wives. The other two husbands agree, sure of winning. Lucentio sends his servant in search of Bianca, but she sends back word that she was busy. Then Hortensio sends for his wife, but the widow replies that if Hortensio wants her, he should come to her. Petruchio then command Kate to come, and, to everyone's amazement, Kate comes immediately, bringing the other two wives, then proceeds to instruct the women on how to have a happy marriage.
The play ends happily, with everyone agreeing that Petruchio and Kate have made a happy marriage.