Understanding natural selection is at the core of many evolutionary and population genetic investigations. However, it is typically difficult to directly detect natural selection. Instead, it has to be inferred from observations of DNA sequence data. In this chapter, we will briefly introduce some standard models of natural selection used in population genetics. We will then review some of the main signatures of selection that can be identified by analyses of DNA sequence data, and finally provide an overview of some of the many different statistical methods that have been developed to identify natural selection. We will argue that the lack of tractable likelihood approaches has spurred a large literature on more ad hoc statistical approaches based on summary statistics.