In heat processing, microbial inactivation is traditionally described as log-linear. As a general rule, the relation between rate of inactivation and temperature is also described as a log-linear relation. The model is also sometimes applied in pressure and in pulsed electric field (PEF) processing. The model has proven its value by the excellent safety record of the last 80 years, but there are many deviations from log-linearity. This could lead to either over-processing or under-processing resulting in safety problems or, more likely, spoilage problems. As there is a need for minimal processing, accurate information of the inactivation kinetics is badly needed. To predict inactivation more precisely, models have been developed that can cope with deviations of linearity. As extremely low probabilities of survival must be predicted, extrapolation is almost always necessary. However, extrapolation is hardly possible without knowledge of the nature of nonlinearity. Therefore, knowledge of the physiology of inactivation is necessary. This paper discusses the physiology of denaturation by heat, high pressure and pulse electric field. After discussion of the physiological aspects, the various aspects of the development of inactivation models will be addressed. Both general and more specific aspects are discussed such as choice of test strains, effect of the culture conditions, conditions during processing and recovery conditions and mathematical modelling of inactivation. In addition to lethal inactivation, attention will be paid to sublethal inactivation because of its relevance to food preservation. Finally, the principles of quantitative microbiological risk assessment are briefly mentioned to show how appropriate inactivation criteria can be set.