Summary
Lucentio, no longer disguised as Cambio, steals away with Bianca to church just before Petruchio, Katharina, Vincentio and Grumio arrive. Vincentio knocks on Lucentio's door, which the Pedant answers. When Vincentio claims to be Lucentio's father, the Pedant denies this and insists that he himself is Lucentio's father. A heated argument ensues and escalates as Vincentio sees Lucentio's servants, Biondello and Tranio, complicit in the deception. Vincentio beats Biondello and accuses Tranio of murdering and impersonating Lucentio. Petruchio and Kate, meanwhile, step aside and enjoy the unfolding farce.
Tranio and Baptista call for an officer, claiming that Vincentio is mad, and the controversy rages until Lucentio and Bianca return from their hasty wedding. Seeing that their game is finally up, Tranio, the Pedant, and Biondello all scatter away. Lucentio pleads for his father's forgiveness, explaining the situation to him and assuring him of Tranio's innocence in the matter. Though still fuming, Vincentio grants his approval of Lucentio and Bianca's union and assures Baptista: "Fear not, [...] we will content you." (5.1: 127) The scene ends with Kate bantering with Petruchio and granting him a reluctant kiss.
In the play's final scene, the assembled company enjoys a banquet in Lucentio's home. There are three newlywed couples - Kate and Petruchio, Lucentio and Bianca and Hortensio and the Widow. The women leave and Baptista remarks that Petruchio has married "the veriest shrew of all." (5.2: 64) Petruchio heartily disagrees, and proposes a wager - the men agree on a hundred crowns - to determine "whose wife is most obedient." (5.2: 67) Both Hortensio and Lucentio bid their wives to come as part of the bargain, and both wives refuse. The one wife who does follow the order is, to all but Petruchio's surprise, Katharina. Petruchio, to prove the point even further, asks Katharina to bring forth the other two wives, which she promptly does. Petruchio then requests that she "tell these headstrong women/What duty they do owe their lords and husbands." (5.2: 134-135) Katharina does as asked, delivering a long speech on a wife's duty to her husband.
Analysis
The crux of most negative criticism of The Taming of the Shrew is Katharina's final monologue. Indeed, it is hard to accept such lines as these: "Such duty as the subject owes the prince,/Even such a woman oweth to her husband;/And when she is forward, peevish, sullen, sour,/And not obedient to his honest will,/What is she but a foul contending rebel/And graceless traitor to her loving lord?" (5.2: 159-164) How are modern audiences to take such a blatant affirmation of sexism, of female subjugation before the male "lord"?
But perhaps we need not take the speech at face value at all. A strong current of irony runs through it. To consider first its role in the dramatic symmetry of the play as a whole, Kate's speech can be read as an answer, from the woman's part, to Lucentio's own opening monologue. These lengthy chunks of speech serve as bookends to the drama. Both follow the mold of classical convention laid out in ancient Greek theater: the expositive salvo at the beginning and the moralistic coda at the end, in which the lessons learned are summarized and the meaning of the play is made clear.
Needless to say, these conventions had been tampered with well before Shakespeare's time. Even the Greeks themselves didn't always rigidly follow them. Nonetheless, Shakespeare went farther than any dramatist before his time in approaching comedy with tongue firmly in cheek. Katharina's closing monologue may be an elaborate joke. Just as Lucentio's lofty language at the play's beginning was coupled with an erotic undertone, so too the pomposity of Katharina's language contrasts with her subject matter.
She repeatedly alludes to royalty and to the machinations of government: "thy lord, thy king, thy governor" (5.2: 142); "thy lord, thy life, thy keeper,/Thy head, thy sovereign" (5.2: 150-151); "tribute" (5.2: 156); "prince" (5.2: 159); "loving lord" (5.2: 164); "rule, supremacy, and sway" (5.2: 167); "duty" (5.2: 182). She invokes war and battle - "our lances" (5.2: 177) - and the hardships of nature - "To painful labor both by sea and land,/To watch the night in storms, the day in cold." (5.2: 153-154) And what is she actually talking about? Marriage. True, marriage may be an important institution, but one would never know it from the way it is treated in Shrew. Courtship and marriage is the butt of jokes, games, disguises, innuendoes. In short, marriage is theater in The Taming of the Shrew. Just so, Katharina's speech, in the context of the play that precedes it, is deeply ironic. It would be one thing if, after subjecting her to such a cruel battery of taming techniques, Petruchio made the speech; but the fact that Katharina is given the last word - and also the longest speech in the play - is itself enough to raise an eyebrow. Perhaps Kate's speech is her way of putting on yet another act, of wryly offering one more illusion. According to this reading, Kate's subjection is a form of grand sarcasm, as she pretends to genuflect before the childish men who have spent so much of the play in comic confusion. This is how you play their game, she seems to say between the lines, and this is how you beat them at it.