Population genomics is the study of the amount and causes of genome-wide variability in natural populations, a topic that has been under discussion since Darwin. This paper first briefly reviews the early development of molecular approaches to the subject: the pioneering unbiased surveys of genetic variability at multiple loci by means of gel electrophoresis and restriction enzyme mapping. The results of surveys of levels of genome-wide variability using DNA resequencing studies are then discussed. Studies of the extent to which variability for different classes of variants (non-synonymous, synonymous and non-coding) are affected by natural selection, or other directional forces such as biased gene conversion, are also described. Finally, the effects of deleterious mutations on population fitness and the possible role of Hill-Robertson interference in shaping patterns of sequence variability are discussed.