Main Index On a Friday 1985-1991 Pablo Honey The Bends OK Computer Kid A Amnesiac Hail to the Thief In Rainbows The King of Limbs A Moon Shaped Pool The Eraser Amok Tomorrow's Modern Boxes Anima Thom Yorke Jonny Greenwood Ed O'Brien Colin Greenwood Philip Selway
Various items from the 'scrapbook' section of radiohead.com are related to the creation of the song:

Q: "Were these songs written in a concentrated period?"

Thom: "Absolutely, except for 'Cymbal Rush' - that riff that had been around for ages - and 'The Eraser', where the piano chords are Jonny's. I recorded them on a dictaphone around his house one day. A year and a half later, I had to own up that I had sampled them, cut them into a different order and made them into a song [laughs]. 'Is that alright? Sorry, Jonny.'"
the first lines you hear on the album are, "please excuse me, but i got to ask, are you only being nice because you want something?/my fairytale arab princess be careful how you respond/you might end up in this song". when asked to comment on the lyrics of "the eraser" there's a long pause before he simply answers, "i can't".
'The Eraser' is the only song from Thom's first solo album, of which no remix was officially released. It is highly likely, though, that Thom commissioned a remix for this song, too. It's possible that he simply didn't like the outcome much and decided to leave this one out. Instead, Cristian Vogel was allowed to contribute two remixes, so that the overall number of remixes matches that of the original album tracks.
There are a few remixes of this song, but none have been released officially. This one, which sounds like it is not just made from the finished mix, but based on its individual components, which Thom had to provide, was done by XXXChange:
There is also this one by Ellen Allien:
On August 2nd 2008, Thom posted a piece called 'Eraser Infinite Mk2' on his page at w.a.s.t.e. central. It's based on the piano chords played by Jonny that Thom had taped with a dictaphone and used as the basis for 'The Eraser'. This would later be re-used in an early version of 'Twist':


Eraser
It took Thom three years following the release of The Eraser to put together a proper tour based on the album. Recruiting Nigel Godrich, Flea, Mauro Refosco and Joey Waronker to form the band, the group played a first set of shows in october 2009 and another in april 2010, initially under the name "?????", since Thom had not yet named the project "Atoms For Peace". The tour ended with a solitary gig in august 2010 in Japan. Each night, the main set would consist of the The Eraser played in its entirety. During this period, Thom also played the song in Cambridge at a Green Party benefit and the 2010 Glastonbury and Big Chill festivals:
On October 2nd 2009, the song had its full band live debut at the Echoplex in Los Angeles at the first gig of Thom's then unnamed band, consisting of himself, Flea, Nigel Godrich, Joey Waronker and Mauro Refosco. By the time they played a proper US tour in spring 2010 they had a name, 'Atoms For Peace'. On the first night of that tour, april 5th 2010 in New York City, there was also an additional trumpet player on stage for the song:

The song was performed live by Thom and Nigel in 2013 as part of their Amok album launch DJ sets:
18. february 22nd 2013 Oval Space London UK Link
19. march 8th 2013 Berghain Berlin Germany Link
20. march 14th 2013 Le Poisson Rouge New York City USA Link
21. april 17th 2013 Razzmatazz Barcelona Spain Link
22. april 19th 2013 Gaîté Lyrique Paris France Link