BSE in cattle, scrapie in sheep and Creutzfeldt-Jakob disease (CJD) in humans are members of a family of fatal neurodegenerative diseases called Transmissible Spongiform Encephalopathies (TSEs) or Prion diseases. They are characterised by a long pre-clinical incubation period and a variable length clinical course determined by the strain of agent and the species of host. They are invariably fatal. The link between BSE in cattle and a variant form of CJD (vCJD) has focused attention on the controls in place to minimise the spread of these agents both within the animal population and to humans. Here the strategies for reducing the transmission of these agents are discussed and the potential for successful eradication of these animal diseases considered.