Among 24 foodborne parasites ranked by FAO/WHO, 15 are associated with food of non-animal origin (FoNAO). Control of these hazards is essential for food safety. Control measures to inactivate parasites in FoNAO are reviewed. Preventing contamination is key to ensuring the safety of fresh produce. However, additional control measures can further reduce the likelihood of occurrence of infectious parasites in FoNAO. Key Findings and Conclusions: The efficacy of treatments depends on parasite species, developmental stage, matrix, and application conditions. Conventional pasteurization (72 °C; 15 s) inactivates parasites in most matrices, although some parasites are more heat resistant, and this may be an inappropriate method for many FoNAO that are intended for eating fresh and raw. Freezing at −20 °C for 2 days inactivates most, but not all, parasites, and some are highly resistant to freezing. Parasites generally survive chemical disinfection, making its application at effective doses often unsuitable at an industrial scale. Ozone and chlorine dioxide are the most promising in terms of efficacy and dosage, nevertheless challenges remain in their application especially for the most fragile produce. High-pressure processing is an efficient technology, providing good inactivation of parasites. Further research should focus on standardizing experimental approaches for evaluation of inactivation techniques and development of methods to measure parasite inactivation in food matrices. •Various parasites can be transmitted to people via foods of non-animal origin (FoNAO).•Potential methods for inactivation of transmission stages in FoNAO are reviewed.•Thermal methods may not be appropriate for FoNAO; some parasites survive freezing.•Chemical methods have mostly been characterised in simple matrices rather than food.•Standardised evaluation methods are lacking, making comparisons difficult.