  What is a population? This review considers how a population may be defined
in terms of understanding the structure of the underlying genetics of the
individuals involved. The main approach is to consider statistically
identifiable groups of randomly mating individuals, which is well defined in
theory for any type of (sexual) organism. We discuss generative models using
drift, admixture and spatial structure, and the ancestral recombination graph.
These are contrasted with statistical models for inference, principle component
analysis and other `non-parametric' methods. The relationships between these
approaches are explored with both simulated and real-data examples. The
state-of-the-art practical software tools are discussed and contrasted. We
conclude that populations are a useful theoretical construct that can be well
defined in theory and often approximately exist in practice.
