The extent to which normal (nonmalignant) cells of the body can evolve through mutation and selection during the lifetime of the organism has been a major unresolved issue in evolutionary and developmental studies. On the one hand, stable multicellular individuality seems to depend on genetic homogeneity and suppression of evolutionary conflicts at the cellular level. On the other hand, the example of clonal selection of lymphocytes indicates that certain forms of somatic mutation and selection are concordant with the organism-level fitness. Recent DNA sequencing and tissue physiology studies suggest that in addition to adaptive immune cells also neurons, epithelial cells, epidermal cells, hematopoietic stem cells and functional cells in solid bodily organs are subject to evolutionary forces during the lifetime of an organism. Here we refer to these recent studies and suggest that the expanding list of somatically evolving cells modifies idealized views of biological individuals as radically different from collectives.