Peste des petits ruminants virus (PPRV) causes a severe contagious disease of sheep and goats and has spread extensively through the developing world. Because of its disproportionately large impact on the livelihoods of low-income livestock keepers, and the availability of effective vaccines and good diagnostics, the virus is being targeted for global control and eventual eradication. In this review we examine the origin of the virus and its current distribution, and the factors that have led international organizations to conclude that it is eradicable. We also review recent progress in the molecular and cellular biology of the virus and consider areas where further research is required to support the efforts being made by national, regional, and international bodies to tackle this growing threat.