Novel pathogens continue to emerge in human, domestic animal, wildlife and plant populations, yet the population dynamics of this kind of biological invasion remain poorly understood. Here, we consider the epidemiological and evolutionary processes underlying the initial introduction and subsequent spread of a pathogen in a new host population, with special reference to pathogens that originate by jumping from one host species to another. We conclude that, although pathogen emergence is inherently unpredictable, emerging pathogens tend to share some common traits, and that directly transmitted RNA viruses might be the pathogens that are most likely to jump between host species.