Phylogenetic trees based on gene sequence data contain information about the evolutionary processes responsible for their genesis. Methods have now been developed which help to reveal those processes. The methods are based on simple models of evolutionary change but, when applied across individuals in a population, rather than across species in a higher-level taxon, they can reveal the past history of population change. Examples from salamanders and viruses are used to illustrate how the past history of changes in speciation rate and the origin of epidemics can be inferred in the absence of fossil material or historical documentation.