Background. Transmissible spongiform encephalopathies (TSEs) or prion diseases are a unique group of neurodegenerative diseases of animals and humans, which always have a fatal outcome and are transmissible among animals of the same or different species. Scope and Approach. The aim of this work is to review some recent data about animal TSEs, with the emphasis on their causative agents and zoonotic potential, and to discuss why the surveillance and control measures over animal TSEs should remain in force. Key Findings and Conclusions. We still have incomplete knowledge of prions and prion diseases. Scrapie has been present for a very long time and controlled with varied success. Bovine spongiform encephalopathy (BSE) emerged unnoticed, and spread within a few years to epidemic proportions, entailing enormous economic consequences and public concerns. Currently, the classical BSE epidemic is under control, but atypical cases do, and probably will, persist in bovine populations. The Chronic Wasting Disease (CWD) of the cervids has been spreading in North America and has recently been detected in Europe. Preventive measures for the control of classical BSE remain in force, including the feed ban and removal of specified risk materials. However, active BSE surveillance has considerably decreased. In the absence of such preventive and control measures, atypical BSE cases in healthy slaughtered bovines might persist in the human food chain, and BSE prions might resurface. Moreover, other prion strains might emerge and spread undetected if the appropriate preventive and surveillance measures were to cease, leaving behind inestimable consequences.