Although panpsychism has had a very long history, one that goes back to the very origin of western philosophy, its force has only recently been appreciated by analytic philosophers of mind. And even if many still reject the theory as utterly absurd, others have argued that it is the only genuine form of physicalism. This paper examines the case for panpsychism and argues that there are at least good prima facie reasons for taking it seriously. In a second step, the paper discusses the main difficulty the theory has to face, the ‘composition problem’. This is the problem of explaining how the primitive experiences that are supposed to exist at the ultimate level of reality could give rise to the unified experience of a human being. What assumptions as to the nature of experience generate the composition problem? Is mental composition impossible in principle or do we simply lack at present any understanding of phenomenal parts and wholes?