As a starting point to this volume, the authors address the fundamental question What underlying forces are responsible for the observed patterns of variability, given a collection of DNA sequences? In approaching this question they introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model and the infinite sites model. They then discuss the complications that come from nonconstant population size, recombination, population subdivision and three forms of natural selection: directional selection, balancing selection and background selection. These theoretical results set the stage for the investigation of various statistical tests to detect departures from neutral evolution.