The ability of a pathogen to cause an epidemic when introduced in a new host population often relies on its ability to adapt to this new environment. Here, we give a brief overview of recent theoretical and empirical studies of such evolutionary emergence of pathogens. We discuss the effects of several ecological and genetic factors that may affect the likelihood of emergence: migration, life history of the infectious agent, host heterogeneity, and the rate and effects of mutations. We contrast different modelling approaches and indicate how details in the way we model each step of a life cycle can have important consequences on the predicted probability of evolutionary emergence. These different theoretical perspectives yield important insights into optimal surveillance and intervention strategies, which should aim for a reduction in the emergence (and re-emergence) of infectious diseases.