The multispecies coalescent (MSC) is an extension of the single-population coalescent model of population genetics to the case of multiple species. The MSC naturally accommodates speciation events (with subsequent genetic isolation between species) and the coalescent process within each species. It provides a framework for analysis of multilocus genomic sequence data from multiple species in a number of inference problems including species tree estimation, accounting for ancestral polymorphism and deep coalescence. Within this framework, the genealogical fluctuations across genes or genomic regions (and the gene tree/species tree conflicts that may result) are not seen as a problem but rather as a source of information for estimating important parameters such as species divergence times, ancestral population sizes, and the timings, directions, and intensities of cross-species introgression or hybridisation events. This chapter outlines the basic theory of the MSC and its important applications in analysis of genomic sequence data, describing the most widely-used full-likelihood and heuristic methods of species tree estimation. We discuss several active areas of research in which we predict future developments will occur, including inference of introgression events on a species phylogeny.