So Thom Yorke has debuted a new backing band for his solo shows, of which members include:

Flea(?!), of the Red Hot Chili Peppers.
Nigel Godrich, long-time producer of Radiohead and Thom's 'Eraser' album as well.
Beck/R.E.M. drummer Joey Waronker.
And Mauro Refosco of Forro in the Dark.
They had an unofficial run-through in Los Angeles at the Echoplex. Four new songs were unveiled, three performed by Thom solo on piano or guitar, and one with the full band ('Judge, Jury & Executioner', which ultra-fans will recognize at the second name for 'Hail to the Thief''s 'Myxomatosis'). I must say that while Radiohead and Thom have announced no plans for new records, we have been lucky to have at least had quite a glut of awesome new songs appear from both entities. Enjoy.
Thom Yorke - Open the Floodgates
Thom Yorke - Lotus Flower Thom Yorke - Skirting the Surface Thom Yorke - Judge, Jury & Executioner
Or you can just download all four
here. Videos below.