Petruchio is a Veronese man who comes to Padua with one purpose: to marry into money. Through his friend Hortensio, he learns about Katherine and decides to make her his wife. Bianca's suitors see Petruchio as an answer to their prayers, since they may not even court Bianca until Katherine is married. After the wedding, Petruchio sets about "taming" Katherine by treating her harshly and pretending to have violent mood swings. Katherine puts up a fight but ultimately gives in.
Katherine, the elder of Baptista Minola's two daughters, is notorious for her shrewish temper. Because of this, her father has a hard time finding a man willing to marry her. When Petruchio takes on the task, she is dismayed and angered by his rude behavior. She eventually gives in to Petruchio's taming efforts, but not without a mighty struggle.
In terms of personality, Bianca is nearly the opposite of her sister. She loves books and music, and her father hires tutors for her to encourage these hobbies. She initially has her doubts about Lucentio but eventually agrees to marry him in secret.
Baptista Minola is a rich Paduan merchant who is anxious to marry off his elder daughter, Katherine. Until a husband is found for Katherine, he refuses to let anyone even court his younger daughter, Bianca. Although Baptista is "an affable and courteous gentleman," he often seems oblivious to his daughters' real wishes, as when he mistakes Katherine's tears of anger for tears of disappointment that her wedding has been cancelled. He is perplexed by Petruchio's bad behavior, but he does nothing to stop his mistreatment of Katherine. Baptista also arranges Bianca's marriage based on money, not love: for him, the man who can pay the biggest dower, money a wife is entitled upon her husband's death, is the ideal son-in-law.
Lucentio is a young man from Pisa who has come to Padua to further his education. He sees Bianca by chance and immediately falls in love. When he learns about her fondness for books and learning, he decides to disguise himself as a language tutor named Cambio. Baptista Minola then hires "Cambio," granting him a chance to court Bianca in secret. Near the end of the play, Lucentio casts off his disguise and elopes with Bianca.
Hortensio, who lives in Padua, is an old friend of Petruchio's. He introduces Petruchio to the idea of wooing Katherine, but when the "taming" begins, he fears his friend has gone too far. Hortensio is also one of Bianca's suitors. Because Baptista Minola will not let him court Bianca openly, he disguises himself as a music teacher and sneaks love poems into Bianca's lessons. He eventually gives up his courtship of Bianca after seeing her with Lucentio.
The loyal Tranio agrees to switch places with his master, Lucentio, enabling him to court Bianca. When Baptista Minola finally agrees to marry Bianca to her richest suitor, Tranio places a winning "bid" on Lucentio's behalf. He then finds a merchant who is willing to pose as Lucentio's father and approve the match.