Understanding how and why humans are biologically different is indispensable to get oriented in the ever-growing body of genomic data. Here we discuss the evidence based on which we can confidently state that humans are the least genetically variable primate, both when individuals and when populations are compared, and that each individual genome can be regarded as a mosaic of fragments of different origins. Each population is somewhat different from any other population, and there are geographical patterns in that variation. These patterns clearly indicate an African origin for our species, and keep a record of the main demographic changes accompanying the peopling of the whole planet. However, only a minimal fraction of alleles, and a small fraction of combinations of alleles along the chromosome, is restricted to a single geographical region (and even less so to a single population), and diversity between members of the same population is very large. The small genomic differences between populations and the extensive allele sharing across continents explain why historical attempts to identify, once and for good, major biological groups in humans have always failed. Nevertheless, racial categorization is all but gone, especially in clinical studies. We argue that racial labels may not only obscure important differences between patients but also that they have become positively useless now that cheap and reliable methods for genotyping are making it possible to pursue the development of truly personalized medicine.