Foodborne viruses, in particular human norovirus and hepatitis A virus, are the most common causes of food-associated infections and foodborne illness outbreaks around the world. Since it is currently not possible to cultivate human noroviruses and the wild-type strain of hepatitis A virus in vitro, the use of a variety of viral surrogates is essential to determine appropriate thermal processing conditions to reduce the risk associated with their contamination of food. Therefore, the objectives of this review are to (i) present pertinent characteristics of enteric foodborne viruses and their viral surrogates, (ii) discuss the viral surrogates currently used in thermal inactivation studies and their significance and value, (iii) summarize available data on thermal inactivation kinetics of enteric viruses, (iv) discuss factors affecting the efficacy of thermal treatment, (v) discuss suggested mechanisms of thermal inactivation, and (vi) provide insights on foodborne enteric viruses and viral surrogates for future studies and industrial applications. The overall goal of this review is to contribute to the development of appropriate thermal processing protocols to ensure safe food for human consumption.