Each of the 14 billion copies of the human genome in the world's population is unique, and forensic scientists use this fact to identify individuals.The differences between genomes are small (about 0.1% on average), but are not randomly distributed, and cluster in different indigenous groups of people (populations). So, despite the fact that small inter--population distances do not support a classical biological definition of races in humans, statistical methods are nonetheless claimed to be able to predict the population of origin of a DNA sample with considerable success. Such methods are employed in the genetic ancestry tests offered to the public, and particular genetic signatures, often in the male--specific Y--chromosome or maternally--inherited mitochondrial DNA, have become widely identified with particular existing or ancestral groups, such as Vikings, Jews, or Zulus, or even specific ancestral individuals. Here, we provide a primer on genetics and genomics, and describe the way in which genetic markers have become associated with particular groups. We describe the conflict between population genetics and individual--based genetics and the pitfalls of the over--simplistic interpretation of genetic data, arguing that although the tests themselves are reliable and scientific, the interpretations are unreliable and strongly influenced by cultural and other social forces.