The study of DNA sequence differences within and between species opened new inroads to the understanding of the history of humans as a species. We have learned that we are remarkably similar to other individuals as well as to our closest primate relatives. To understand what makes us unique, both as individuals and as a species, we need to consider the genome as a mosaic of discrete segments, each with its own unique history and relatedness to other individuals, to ancestral relatives and to other species. I will discuss what studies of genetic variation among humans and between humans and our extinct relative, the Neanderthal, has told us about human population history and include consideration of recent discussions of whether racial ‘classification’ of humans has any genetic validity. I will also describe work demonstrating that despite the fact that the DNA sequences of humans and chimpanzees differ only slightly, activity levels of a sizable proportion of genes differ between humans and chimpanzees. I will also highlight results on the evolution of the first gene known to be involved in the ability of humans to use articulate language.