Lucenctio and Tranio arrive in Padua. They have travelled there because Lucentio is planning to study at the university, or the ‘nursery of arts’, and his loyal servant has accompanied him.

Baptista, a wealthy merchant, announces that he will not allow his younger daughter Bianca to marry until her older sister Katherina is married. Bianca has a number of suitors who want to marry her, including Gremio and Hortensio, but Katherina is described as a ‘fiend of hell’ who no one wants to marry. Lucenctio is hidden nearby and overhears this. However, he also sees Bianca and falls in love with her 'sweet beauty'.

Lucentio disguises himself as a schoolteacher, Cambio, so he can be closer to Bianca, who is still allowed tutors. To help him, Tranio puts on his master’s clothes and disguises himself as Lucentio. Dressed as Cambio, Lucentio asks Gremio to introduce him to Baptista, saying that he will convince Bianca of Gremio’s love for her through his lessons.

Petruchio arrives in Padua. He has travelled from Verona, along with his servant Grumio, because he wants to find a rich wife. He hears about Katherina from his friend Hortensio and decides to take on the challenge of marrying her, especially as ‘she shall be rich, /And very rich!’

Hortensio also decides to disguise himself as a schoolteacher, Licio, to gain access to Baptista’s household. Just like Lucentio, he thinks this is the best way to get close to Bianca and convince her of his love.

Katherina ties up and bullies her sister Bianca, to find out which suitor Bianca prefers. Bianca says she has yet to see that ‘special face’. Baptista feels ‘grieved’ at his eldest daughter’s behaviour and does not know what to do. Katherina is annoyed at her father’s preference for Bianca.

Both Cambio (actually Lucentio) and Licio (actually Hortensio) are welcomed as teachers into Baptista’s house. Hortensio struggles to teach Katherina, who breaks a lute over his head.

Petruchio asks Baptista if he can marry Katherina and they agree a financial deal. Baptista warns Petruchio against the match and only agrees to it on the condition that Petruchio first wins Katherina’s love. Katherina and Petruchio then meet for the first time, and cleverly spar with each other. Petruchio tells her that he will marry her, even though she objects and tells him to fear her waspish ‘sting’.

Petruchio goes back to Verona, telling Baptista he will return on Sunday for his wedding to Katherina. He tells Baptista to go ahead with preparations.

With Katherina engaged, Bianca is now free to marry. Baptista asks Gremio and ‘Lucentio’ who can offer his daughter most wealth. Tranio, disguised as ‘Lucentio’, offers more money. Baptista agrees to the marriage between 'Lucentio' and Bianca, although says he must have Lucentio’s father’s assurance of the money first. Tranio begins to plan how they can trick Baptista by finding someone who can pretend to be Lucentio’s father.

During a Latin lesson, the real Lucentio reveals his true identity to Bianca and tells her he wants to marry her. Bianca is cautious but keeps his secret. Moments later, Hortensio also reveals his true identity to Bianca through a music lesson, but she pretends to not understand.

Petruchio arrives late for his wedding to Katherina, wearing strange clothes and behaving inappropriately. Katherina is deeply embarrassed by this ‘rudesby’ but the guests and her father seem to overlook his slights once the ceremony is over. Petruchio then says that they must leave immediately for his house in Verona, rather than stay for the wedding feast.

Lucentio and Tranio plan to get an old man to pretend to be Vincentio, Lucentio’s father. They need to convince Baptista of Lucentio’s financial status in order for him to agree to the marriage of Lucentio and Bianca. They convince a merchant to help them with their plan.

In Verona, Petruchio denies his new wife Katherina food and sleep. He says the food is burnt and sends it away, confusing Kate with his behaviour. He tells the audience that he will train, or man, her like a falcon and change her into an obedient wife.

Hortensio sees Bianca talking to ‘Cambio’ and decides she is unconstant. Encouraged by Tranio, he decides to give up on pursuing Bianca and marry a widow who has been in love with him for a long time.

Katherina is still being denied food. Petruchio confuses her further by bringing her beautiful clothes and then sending them away, saying they are not good enough for her.

Tranio, still disguised as Lucentio, tricks a visitor to Padua into pretending to be Lucentio’s father, Vincentio. He then tricks Baptista into believing the man is the wealthy Vincentio. After meeting him, Baptista agrees the terms of Bianca’s marriage.

Travelling back to Padua, Katherina challenges Petruchio’s statements that the moon is the sun. He says they will turn back unless she agrees it is the moon. Katherina relents and says to her husband it is ‘what you please’. On their way, they meet the real Vincentio, Lucentio’s father, who is on his way to visit his son.

Lucentio and Bianca elope to marry in secret, leaving Tranio, disguised as Lucentio, and the merchant, disguised as Vincentio, in Lucentio’s house.

The real Vincentio arrives in Padua looking for his son. When he finds Tranio and the merchant claiming to be Lucentio and himself, he accuses them of murdering his son. Lucentio arrives just in time and explains the truth. He then reveals that he and Bianca have married.

The three newly married men, Petruchio, Lucentio and Hortensio, place a bet that their wives will come to them on their command. Both Lucentio’s wife, Bianca, and Hortensio’s wife refuse. However, Katherina comes as soon as Petruchio calls for her. She tells the other women why they should obey their husbands and no one can believe how changed she is.