High‐pressure processing (HPP) is a non‐thermal treatment in which, for microbial inactivation, foods are subjected to isostatic pressures (P) of 400–600 MPa with common holding times (t) from 1.5 to 6 min. The main factors that influence the efficacy (log10 reduction of vegetative microorganisms) of HPP when applied to foodstuffs are intrinsic (e.g. water activity and pH), extrinsic (P and t) and microorganism‐related (type, taxonomic unit, strain and physiological state). It was concluded that HPP of food will not present any additional microbial or chemical food safety concerns when compared to other routinely applied treatments (e.g. pasteurisation). Pathogen reductions in milk/colostrum caused by the current HPP conditions applied by the industry are lower than those achieved by the legal requirements for thermal pasteurisation. However, HPP minimum requirements (P/t combinations) could be identified to achieve specific log10 reductions of relevant hazards based on performance criteria (PC) proposed by international standard agencies (5–8 log10 reductions). The most stringent HPP conditions used industrially (600 MPa, 6 min) would achieve the above‐mentioned PC, except for Staphylococcus aureus. Alkaline phosphatase (ALP), the endogenous milk enzyme that is widely used to verify adequate thermal pasteurisation of cows’ milk, is relatively pressure resistant and its use would be limited to that of an overprocessing indicator. Current data are not robust enough to support the proposal of an appropriate indicator to verify the efficacy of HPP under the current HPP conditions applied by the industry. Minimum HPP requirements to reduce Listeria monocytogenes levels by specific log10 reductions could be identified when HPP is applied to ready‐to‐eat (RTE) cooked meat products, but not for other types of RTE foods. These identified minimum requirements would result in the inactivation of other relevant pathogens (Salmonella and Escherichia coli) in these RTE foods to a similar or higher extent.