The cross‐species transmission of viruses into new host populations, termed virus emergence, is a significant issue in public health, agriculture, wildlife management, and related fields. Virus emergence requires overlap between host populations, alterations in virus genetics to permit infection of new hosts, and adaptation to novel hosts such that between‐host transmission is sustainable, all of which are the purview of the fields of ecology and evolution. A firm understanding of the ecology of viruses and how they evolve is required for understanding how and why viruses emerge. In this paper, I address the evolutionary mechanisms of virus emergence and how they relate to virus ecology. I argue that, while virus acquisition of the ability to infect new hosts is not difficult, limited evolutionary trajectories to sustained virus between‐host transmission and the combined effects of mutational meltdown, bottlenecking, demographic stochasticity, density dependence, and genetic erosion in ecological sinks limit most emergence events to dead‐end spillover infections. Despite the relative rarity of pandemic emerging viruses, the potential of viruses to search evolutionary space and find means to spread epidemically and the consequences of pandemic viruses that do emerge necessitate sustained attention to virus research, surveillance, prophylaxis, and treatment.