In recent years, several foodborne viruses’ outbreaks have been recorded worldwide. Μost of the foodborne viruses have a low infection dose, are stable and can persist and survive in foods for a long time without loss of infectivity. The most important foodborne viruses are: human norovirus (HuNoV), human rotavirus (HRV), hepatitis A virus (HAV), hepatitis E virus (HEV), human astrovirus (HAstV), Aichi virus (AiV), sapovirus (SaV), human adenovirus (HAdV) and enterovirus (EV). In recent years, innovative non-thermal food-processing technologies including high-pressure processing (HPP), cold plasma (CP), ultraviolet light (UV), irradiation and pulsed electric field (PEF) for improving the quality and safety of foods, including foods of animal origin, have been under research. This review presents the recent data on foodborne viruses and reviews the innovative non-thermal technologies for the control of the foodborne viruses in foods.