The story involves the production of a musical version of William Shakespeare's The Taming of the Shrew and the conflict on and off-stage between Fred Graham, the show's director, producer, and star, and his leading lady, his ex-wife Lilli Vanessi.

A secondary romance concerns Lois Lane, the actress playing Bianca, and her gambler boyfriend, Bill, who runs afoul of some gangsters.

The original production starred Alfred Drake, Patricia Morison, Lisa Kirk and Harold Lang.

Producer Arnold Saint-Subber conceived the idea for Kiss Me, Kate after witnessing the on-stage/off-stage battling of husband-and-wife actors Alfred Lunt and Lynn Fontanne during their 1935 production of The Taming of the Shrew.

In writing the lyrics for Kiss Me, Kate, Porter drew from Shakespearean themes and language, without creating something esoteric, and the song "Always True to You in My Fashion" was inspired by the Ernest Dowson poem "Non Sum Qualis Eram Bonae Sub Regno Cynarae”, with its refrain "I have been faithful to thee, Cynara, in my fashion".

Directed by John C. Wilson with choreography by Hanya Holm, the original cast included Alfred Drake, Patricia Morison, Lisa Kirk,[7] Harold Lang, Charles Wood and Harry Clark.

Directed by Sam Spewack with choreography again by Holm, this production starred Patricia Morison, Bill Johnson, Adelaide Hall and Julie Wilson.

The original Australian production played from February 1952 at His Majesty's Theatre, Melbourne, before seasons in Sydney, Brisbane, Perth and Adelaide until 1954.

The cast featured Emile Belcourt (Petruchio), Judith Bruce, Eric Shilling, Ann Howard (Kate), Francis Egerton and Robert Lloyd, with direction by Peter Coe and choreography by Sheila O'Neill.

[18] Directed by Adrian Noble and staged by Ron Field, the production starred Nichola McAuliffe and Paul Jones as Lilli/Kate and Fred/Petruchio, with Tim Flavin and Fiona Hendley as Bill/Lucentio and Lois/Bianca.

[21] A Broadway revival opened at the Martin Beck Theatre on November 18, 1999, and closed on December 30, 2001, after 881 performances and 28 previews.

[26] The production was revived at London Coliseum briefly in June 2018, following a return visit to Leeds Grand Theatre in May 2018.

The Roundabout Theatre Company presented a revised third Broadway revival of Kiss Me, Kate with Kelli O'Hara as Lilli Vanessi/Kate, Will Chase as Fred Graham/Petruchio, Stephanie Styles as Lois Lane/Bianca, and Corbin Bleu as Bill Calhoun/Lucentio.

The production is directed by Scott Ellis and choreographed by Warren Carlyle,[27] with minor "feminist" updates by Amanda Green to make the musical "more accessible for today’s audiences".

Other cast members included Charlie Stemp as Bill / Lucentio, Georgina Onuorah as Lois / Bianca, and Nigel Lindsay and Hammed Animashaun as the gangsters.

Egotistical Fred Graham is the director and producer and is starring as Petruchio, and his movie-star ex-wife, Lilli Vanessi, is playing Katherine.

The two seem to be constantly arguing, and Lilli is particularly angry that Fred is pursuing the sexy young actress Lois Lane, who is playing Bianca.

They recall the operetta in which they met, which included "Wunderbar", a Viennese waltz; they end up fondly reminiscing and singing and dancing.

She walks on stage off-cue and begins hitting Fred, who, along with the other actors, tries to remain in character as Baptista gives Petruchio permission to marry Kate.

Back onstage, Bianca and Lucentio dance while the chorus performs "We Sing of Love", covering a scene change.

Paul (Fred's assistant) and other crew members lament that it's "Too Darn Hot" to meet their lovers that night.

There have been at least four television productions, the first on Hallmark Hall of Fame in 1958, with Drake and Morison reprising their Broadway roles,[40] the second recorded for the launch of BBC Two in the UK in 1964, starring Howard Keel, Patricia Morison and Millicent Martin, the third in 1968 with then husband-and-wife team Robert Goulet and Carol Lawrence, and the fourth in 2003 on Great Performances, a high-definition shot performance of the London revival with Brent Barrett and Rachel York.