The bovine spongiform encephalopathy (BSE) epidemic in cattle has had a huge economic impact on the agricultural industries across Europe. Furthermore, scientific evidence now strongly supporting a link between a new variant of Creutzfeldt-Jakob disease (vCJD) and consumption of BSE-infected animals has further heightened the need both to understand the transmission of these new diseases and to improve control measures to protect public health. In this paper we review work undertaken by our group using epidemiological models to understand the transmission dynamics of BSE and vCJD. We present new estimates of the future number of cases of BSE and the number of infected animals slaughtered for consumption for Great Britain, and summarise similar analyses undertaken for Northern Ireland, Ireland, Portugal and France. We also consider the epidemiological determinants of the future course of the vCJD epidemic, including the age and genetic characteristics of the confirmed cases, and present predictions of future case numbers.