The economic consequences of livestock epidemics have been long studied for purposes of estimating the costs of preventive and curative veterinary measures. In this paper, we show that this catastrophic risk may have wide market consequences, and that the risk management systems are quite limited to compensate long term impacts in the European context of growing trade. Through a detailed literature review, we present the main developments of the economic research aiming at highlighting the economic consequences of animal epidemics such as Foot and Mouth Disease. We acknowledge that a very few studies have focused on the economic dynamics and on the long-run effects occurring after an epidemic disease outbreak. We discuss the relevance of a dynamic approach to reveal that the de-structuring of livestock markets affects the production dynamics as well as the whole agricultural sector. Financial implications and market constraints remain poorly studied in the livestock epidemics literature. We emphasize the growing interest of a dynamic Computable General Equilibrium approach to reveal the overall effects of epidemic outbreaks on the whole economy. This innovative research raises important challenges for the assessment and implementation of risk management policies.