The critic Douglas Wolk described the song as "a truly shameless ripoff of The Isley Brothers' 1959 hit "Shout"... basically the fast parts of "Shout" with the gospel inflections removed and the word 'shimmy' added."^[2] Wolk argues that Brown and The Famous Flames probably performed "Shout and Shimmy" in the October 24, 1962 concerts at which Live at the Apollo was recorded, but that it was left off of the album to prevent sales competition with the studio version of the song. Evidence to support this contention includes the fact that Brown customarily began his concerts with his latest hit (which "Shout and Shimmy" was at the time), and the presence of "Shout and Shimmy"'s a cappella opening ("You know I feel all right...") immediately before the first song on the album, "I'll Go Crazy". James and The Famous Flames sang and performed this song on Dick Clark's American Bandstand,on a telecast dated June 11, 1962.^[3] A performance of "Shout and Shimmy" was the first track on Brown & The Flames' next live album, 1964's Pure Dynamite! Live at the Royal, featuring a comedy skit between Brown and Famous Flame Bobby Bennett.

In two days during 12 to 14 April 1965, British rock group the Who recorded "Shout and Shimmy" as the B-side to their fourth single (third single under the name 'the Who') "My Generation", which was released on October 29, 1965.^[4] The A-side reached number 2 in the United Kingdom,^[5][6] but only reached number 74 on the Billboard Hot 100 and number 99 in Cashbox magazine.^[7][8] The song was part of the Who's repertoire from late 1964, along with several other rhythm and blues covers, including other songs by James Brown. It was ultimately dropped in 1966 once the group had written enough original material.^[9] Several other songs were recorded during the same session as "Shout and Shimmy", including "I'm a Man", "Leaving Here", "Anyway, Anyhow, Anywhere" and two other songs written by Brown: "Please, Please, Please" and "I Don't Mind".^[10]

Their version is undisputedly greatly derived from "Shout", a song by the Isley Brothers made famous by Lulu and the Luvvers, including call- and-response lyrics throughout, similar to other songs by the group at the time, including "Anyway, Anyhow, Anywhere".^[11] In the US however, "Shout and Shimmy" was not released as the B-side of "My Generation", and was instead substituted by "Out in the Street", which later appeared on their debut album My Generation.^[12] On this release the song is dubbed "Out in the Street (You're Going to Know Me)."^[13] "Shout and Shimmy" became a rare collectible in the US, since it wasn't included on the equivalent version of My Generation released in America, The Who Sings My Generation, and instead would remain unissued until it was belatedly released as the opening song to Who's Missing, a collection of rare tracks by the Who was released in 1985.^[14][15]

An archival live performance was eventually released in the 1979 film The Kids Are Alright, but it was not included in the soundtrack album for that movie. It has since been included on reissues and remasters of the album My Generation.^[16] Ultimate Classic Rock ranked it 130 on their list of All 245 Who Songs Ranked Worst to Best in 2018, stating "A party record that captures an element of how frenetic these James Brown covers must have sounded at early Who gigs. A whole mess of fun.^[17]