It has been suggested that evolutionary changes in gene expression account for most phenotypic differences between species, in particular between humans and apes. What general rules can be described governing expression evolution? We find that a neutral model where negative selection and divergence time are the major factors is a useful null hypothesis for both transcriptome and genome evolution. Two tissues that stand out with regard to gene expression are the testes, where positive selection has exerted a substantial influence in both humans and chimpanzees, and the brain, where gene expression has changed less than in other organs but acceleration might have occurred in human ancestors.