In terms of their impact on livestock, and therefore on human well-being and development, rinderpest virus (RPV) and peste des petits ruminants virus (PPRV) are two of the most important members of the paramyxovirus family. RPV, the cause of the most feared of all cattle diseases, now appears to have been eradicated; however, over the past 20 years, PPRV has increased its global distribution through most of sub-Saharan and North Africa, the Middle East, the Indian sub-continent and eastwards into Tibet. While most scientific effort has been focused on developing means of control of the diseases, effort in a small number of laboratories has thrown light on the detailed molecular biology of the viruses, providing information on those areas in which they are the same as, or differ from, other members of the same genus. Such findings have highlighted how important it is to understand the way that these viruses are restricted in the range of organisms in which they will cause disease, an understanding that will become increasingly important with the success in eradicating these diseases on a local and global level.