Radiohead Fans, music critics, and fellow musicians tend to regard them as among the most fearlessly creative bands of their era, although they are not universally popular. In general, Radiohead's music is more complex than that of other pop musicians, incorporating a wide range of influences across genres and time periods, but they identify with the punk and post-punk movements rather than with progressive rock.

Radiohead have sometimes been cited as an "outsider" band within the mainstream, or vice versa. Some fans assume the band to be the natural inheritors of the mantle of R.E.M., Pink Floyd or even The Beatles, though Radiohead have not enjoyed the same commercial success as these groups; Pink Floyd's Dark Side Of The Moon has so far sold over 40 million copies worldwide (and the band have been very quick to publicise those figures), whereas Radiohead's much-acclaimed OK Computer has probably only sold a fraction of that (no official figures exist for OK Computer's success as far as units go). However, reportedly members of these bands cited Radiohead numerous times as one of the greatest modern rock bands. Examples include Michael Stipe (who at a point in time was a quasi-mentor to Thom) is a great fan of the band's output, and Paul McCartney, who lists them as one of his personal favourite acts.

Thom Yorke and Jonny Greenwood are chiefly responsible for songwriting, with Yorke initiating a song and Greenwood developing it, though the entire band is often involved. They all contribute lyrical and artistic ideas to each step of writing and recording music.

All five members are highly respected musicians. Jonny Greenwood in particular is an incredibly talented and versatile musician; he is currently the BBC's Composer in Residence and is adept at numerous instruments aside from the guitar, notably the Ondes Martenot, harmonica and many that have never been recorded. Ed O'Brien, apart from his normal duties as guitarist, is a gifted drummer as well.

This versatility and openness in the band has grown more pronounced over time. In recent years, especially, band members have embraced less clearly defined roles in the band. For example, bassist Colin Greenwood wrote much of "Dollars & Cents", a track on Amnesiac, by playing string samples from Alice Coltrane's work on top of a simple bassline, inspiring his brother Jonny's subsequent arrangement. Yorke switched to bass guitar on the song "The National Anthem". During an average live show one can expect all of them, with the exception of drummer Selway, to play an assortment of instruments.

Early influences include The Beatles, Cardiacs (whom the band supported early in their career), The Smiths, Elvis Costello, Joy Division, Pixies, Talking Heads, Roxy Music, R.E.M., and the Jam, among others. Later influences have included jazz musicians like Charles Mingus, Miles Davis, Ornette Coleman and Krautrock pioneers such as Kraftwerk, Neu! and Can, whose song "Thief" Radiohead have covered live. Electronic music artists like Aphex Twin, Squarepusher, and Autechre have also been cited as important influences on Kid A and Amnesiac. The work of Polish composer Krzysztof Penderecki informed some of Radiohead's string-oriented songs such as How To Disappear Completely, but more significantly, French composer Olivier Messiaen, who made much use of the Ondes Martenot, is a longtime idol of Jonny Greenwood, whose work is held in high regard by the band. Members of Radiohead are also fans of reggae, dub reggae, and classic soul music, particularly Booker T & the MGs for Colin. The band have expressed love for OutKast and old school hip-hop. Artists they have invited to open for them on tour include Sigur Rós, Supergrass, Spiritualized, Sparklehorse, Stephen Malkmus (of Pavement), Low, Clinic, Four Tet and the Beta Band, among others.

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