Lucentio and Hortensio, disguised respectively as Cambio and Litio, vie for the attention of the fair Bianca. Bianca seems thoroughly amused by the competition, and decides that Lucentio may lecture her while Hortensio tunes his lute; once the instrument is in tune, Hortensio may then take over the lesson. Lucentio leaps into action with his "lesson," confessing his identity and his love under the guise of a Latin translation. Bianca responds with her own variant of the game, telling him, through her own "translation," that she does not know him and cannot trust him - but that he should "despair not." (3.1: 44) Hortensio fares less well than Lucentio when he tries to confess his love through a scale on the lute. Bianca dismisses the rouse and all but Hortensio exit at a servant's bidding to help prepare Katharina's room for her wedding tomorrow. Alone on stage, Hortensio notes that Cambio appeared to be courting Bianca, and declares that if Bianca is unable to be faithful to him, he won't be faithful to her either.
The next day, the company all wait in preparation for Katharina's wedding. Petruchio, however, is no where to be seen. Katharina, for her part, breaks down and runs from the scene weeping, and for once Baptista sympathizes with her. At that moment Biondello rushes in and says that Petruchio is on his way, wearing outrageously distasteful clothes, riding a diseased horse only a step away from death, and accompanied by a servant as badly dressed as his master. When Petruchio finally appears, with Grumio at his side, his appearance lives up to Biondello's fanciful account. Baptista and the others are mortified. Petruchio, however, refuses to dignify his appearance, and they follow him to his wedding.
Lucentio and Tranio remain while the rest attend Petruchio's wedding. Tranio explains that Baptista requires Vincentio's assurance and declares his intention to disguise someone as Vincentio. Their plotting is cut short, however, as Gremio appears and provides a detailed account of the raucous wedding, wherein Petruchio scandalized the company.
The wedding party arrives and Petruchio claims that he must leave and cannot stay for his own wedding dinner. Katharina entreats that her husband wait for her. However, Petruchio sweeps Katharina away dramatically. The scene ends with the dazed Baptista telling Tranio that the feast will go on as planned, and that he and Bianca may take the seats of the bride and bridegroom.
Having spent some time with the disguised Tranio, the audience is now shown Lucentio's acting abilities as Cambio. It is appropriate that Lucentio has disguised himself as a scholar, for he originally claimed to come to Padua to pursue education. Just as Tranio uses lofty language to contribute to the illusion of nobility, Lucentio uses lofty Latin words to sneak in the truth of his pursuit of Bianca. Thus the tension between superficial education and below-the-surface desire continues.
The Latin passage that Lucentio pretends to translate for Bianca is fitting, as it describes Priam's palace, thus evoking several Classical images of lust. The Trojan War began with Paris's abduction of Helen - just as Lucentio intends to "abduct" Bianca. Also, that war was won with the Trojan Horse; Lucentio is, in his way, a Trojan Horse wheeled into the enemy's gates under the guise of a gift. Moreover, the name "Priam" evokes phallic imagery, as the Greek god of fertility was called Priapus.
That Lucentio is able to use legitimate figures and allusions to Greek history in order to woo Bianca furthers the tendency in Shrew to balance erudition and lust. He has not strayed far from his intention to pursue education, yet he finds himself embroiled in an undercover seduction. Shakespeare, it seems, prefers living the passions and lessons of the ancients to merely reading about them. In his way, Lucentio is merely living out Tranio's advice at the play's opening - he's mixing pleasure with academics, or, as Tranio put it, mixing Ovid with Aristotle. This could be taken as a motto for the play as a whole, which mixes the bawdiness and eroticism of Ovid with the Classical orderliness of Aristotle's rules of drama.
Hortensio is not as successful as Lucentio in balancing his roles as teacher and wooer. Where Lucentio speaks his words of love to Bianca, Hortensio writes them; where Lucentio reveals himself for who he truly is, Hortensio never does. Bianca's hint to Lucentio - "despair not" - suggests that his method may be working; she offers no such consolation to Hortensio. She does not smash his lute against his head, as Katharina did, but her words strike nearly as fierce a blow: "Call you this gamut? Tut, I like it not./Old fashions please me best; I am not so nice/To change the true rules for odd inventions." (3.1: 78-80)
Her invocation of "old fashions" lingers in the mind, especially when Petruchio appears in the following scene. His behavior flouts convention and tradition at every opportunity: he is tardy, when he does appear he's dressed outlandishly, he curses in church and he refuses to stay for his own wedding dinner. This strategy of exagerrating his beastliness as much as possible is designed to tame Katharina. Indeed, that famous convention-flaunter and "scold" is unable to get a word in edgewise; she is reduced to defending the status quo against Petruchio's outrageousness. His bombast overwhelms her capacity for bombast. She does try to reassert her power, insisting that Petruchio remain for the wedding feast: "Father, be quiet. He shall stay my leisure" (3.2: 217). But her refusal to be subjugated only spurs Petruchio to even more outrageous behavior, as he orders Grumio to draw his sword and steals away with Katharina from the threat of "thieves." (3.2: 236) His closing line is full of pompous masculinity and false chivalry: "Fear not, sweet wench, they shall not touch thee, Kate!" (3.2: 238)
However obvious Petruchio's dominance appears, there is ambiguity in who really has the upper hand as the scene ends. Old Gremio remarks, "I warrant him, Petruchio is Kated." (3.2: 245) This suggests many interpretations. Perhaps he means that Petruchio is in store for a severe scolding. Perhaps that it is Petruchio who has been swept away by Kate - and not the other way around. But most likely of all, it seems, is that Petruchio, in adopting the bombastic ways of his wife, has been more changed by her than she has by him. Shakespeare's exploration of their power struggle continues in the final Acts of the play.