Phylogenetic and epidemic modeling of rapidly evolving infectious diseases

► Rapidly evolving viruses have the same timescale for their ecology and evolution. ► Coalescent analyses have shed much light on virus evolution and population history. ► The nascent field of phylodynamics unifies evolutionary and epidemiological models. ► Current modeling advances focus on the spatially distributed nature of epidemics. ► Darwinian selection in all its forms is a key challenge for phylodynamic methods.