Viruses are an important cause of human disease, often because they are highly transmittable from human to human. A key tool from population genetics that can be applied to the study of viruses is coalescent theory. Coalescent theory predicts genealogical tree shapes as a function of how the studied organisms are evolving. Therefore, under its model assumptions, coalescent theory can be used to infer aspects of the demographic history of evolving organisms. For example, there are characteristics of tree shapes that imply whether the organism population has been constant, growing, or shrinking in size over time. This chapter reviews some of the successes of coalescent theory in the context of inferring aspects of virus evolution, using human immunodeficiency (HIV) and influenza viruses as case studies. Next, the chapter describes limitations of coalescent theory, even as extended to allow some forms of selection, population subdivision, and viral recombination. The relatively new goal to predict influenza virus evolution (rather than infer past evolution) is used to emphasize modeling needs beyond standard or extended coalescent theory models. A new small-scale simulation that combines viral fitness with demographic population structures such as family and work groups is then described as an example extension to coalescent theory models. Prediction goals include early detection of highly lethal new strains and improved vaccine designs that anticipate future evolutionary directions. Regardless which evolutionary model is used to predict virus evolution, because real virus evolution is complex beyond current understanding, there will be substantial model error. Model error, model parameter estimation error, and purely random effects can combine to make some forecast goals unattainable. In these cases the most appropriate prediction is similar to what is often said about stock markets: there will be change.