Abstract The interpretation of evidence is rooted in population genetics theory. The fundamental principle that underpins this is the Hardy–Weinberg equilibrium. The inheritance of genes follows laws of probability that enable probability estimates to describe the “rarity” of a DNA profile. Such calculations rely upon the Hardy–Weinberg equilibrium assumption of “independence”, i.e., that populations are very large, randomly interspersed and randomly mating. However, such assumptions are rarely justified—populations are structured into “sub-populations”; the frequencies of their alleles differ. To compensate, the FST statistic is used as a measure of population differentiation. There are initiatives to collate data to provide community population databases that can be accessed, for example, STRidER acts as a platform that is used as a repository that are subject to rigorous quality control before release. The likelihood ratio is fundamental to all aspects of interpretation of forensic evidence. Likelihood ratios are very flexible. In particular, they can be used to evaluate DNA mixtures, which are the subject of much of the material to be found in subsequent chapters. The early genetics theory applied to mixtures is described, limited to two-contributors. The calculations are very complex. The need for computer algorithms to take over the burden of calculation are described, and there is a demonstration of the principle of extension of multiple contributors. A list of software available to carry out analysis of mixtures is provided. Finally, extension of the theory to relatedness (kinship) tests is introduced.