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This article is part of a collection entitled "Models for Safety, Quality, and Competitiveness of the Food Processing Sector," published in Comprehensive Reviews in Food Science and Food Safety. It has been peer-reviewed and was written as a follow-up of a pre-IFT workshop, partially funded by the USDA NRI grant 2005-35503-16208.ABSTRACT: This article discusses the possibilities to study relevant quality aspects of food, such as color, nutrient content, and safety, in a quantitative way via mathematical models. These quality parameters are governed by chemical, biochemical, microbial, and physical changes. It is argued that the modeling of such quality aspects is in fact kinetic modeling. Therefore, attention is paid to chemical kinetics, and its possibilities and limitations are discussed when applied to changes occurring in foods. The discussion is illustrated with examples from the literature. A major difficulty is that principles from chemical kinetics are strictly speaking only valid for simple elementary reactions, and foods are all but simple. Interactions in the food matrix and variability are 2 complicating factors. It is discussed how this difficulty can be tackled, and research priorities are suggested to come to better models in food science, and thereby to a better control of food quality.