The first part of the title was the title of a paper published more than 20 years ago by Doolittle and Sapienza (1). The main point of that paper was that natural selection can act at more than one level and that the "function" of some structures or processes are best explained by selection operating at a level other than the phenotype of the organism. Said in another way, this means that if you wish to define the "true" function of a structure or process (that purpose for which it was selected during evolution), you must define the nature and the target of the selective force that resulted in the fixation of that structure or process. In this presentation we will focus briefly on two processes, genome imprinting and maternal meiotic drive, that are likely to be examples of natural selection operating on epigenetic features of chromosome structure during meiosis. Although the specific targets of the selective force may be different in each case (pairing elements in the case of genome imprinting, and centromere function in the case of meiotic drive), the selective force at work in both cases is an immediate effect on chromosome segregation. This selective force can be shown to have had a dramatic effect on the evolution of the mammalian karyotype. It also provides a unifying hypothesis for the origin of imprinting in mammals, as well as parental origin effects in organisms in which parental origin-dependent transcriptional silencing has not been observed.