In this paper, the concept “ancestry” is clarified, distinguishing between two notions often confused: genealogical ancestry and genetic ancestry. Genealogical ancestry refers to the identifiable ancestors in a person's family tree. Usually, these are one's parents, grandparents, and great-grandparents, but it is possible that someone finds information about ancestors further back in time through written records or other sources. In contrast, genetic ancestry does not refer to one's family tree, but to the paths through which one's DNA was inherited from one's ancestors. The concept “admixture” is also clarified. There are at least two key issues with this concept, which has its origins in nineteenth-century racial science. One is that describing admixture requires positing imagined “pure” source populations. For instance, to make sense of what it means for someone to be “1/3 African, 2/3 European,” one should be able to clearly define what it means to be 100% African and 100% European. Another issue is that in population genomics, ADMIXTURE plots are sensitive to sampling and model choices. To address these problems, scientists should rethink how they describe human difference: recognize census and ethnic categories as social constructs; stress that human genetic variation is clinal and samplingdependent; replace ancestry labels with explicit statements of genetic similarity to defined reference samples. With these clarifications, this paper also provides the theoretical background for the two subsequent empirical papers.