Radiohead albums feature Greenwood's string and brass arrangements, and he has composed for orchestras including the London Contemporary Orchestra and the BBC Concert Orchestra. His first solo work, the soundtrack for the film "Bodysong," was released in 2003. In 2007, he scored "There Will Be Blood", directed by Paul Thomas Anderson, and has composed the soundtrack for every Anderson film since; in 2018, he was nominated for an Academy Award for his score for Anderson's "Phantom Thread". Greenwood's other scores include two collaborations with director Lynne Ramsay. He has collaborated several times with the Israeli composer Shye Ben Tzur, including on the 2015 album "Junun".