This series of two papers deals with the theory of cell division and its implementation in an individual-based modeling framework. In this first part, the theory of cell division is studied on an individual-based level in order to learn more about the mechanistic principles behind microbial lag phenomena. While some important literature on cell division theory dates from 30 to 40 years ago, until now it has hardly been introduced in the field of predictive microbiology. Yet, it provides a large amount of information on how cells likely respond to changing environmental conditions. On the basis of this theory, a general theory on microbial lag behavior caused by a combination of medium and/or temperature changes has been developed in this paper. The proposed theory then forms the basis for a critical evaluation of existing modeling concepts for microbial lag in predictive microbiology. First of all, a more thorough definition can be formulated to define the lag time lambda and the previously only vaguely defined physiological state of the cells in terms of mechanistically defined parameters like cell mass, RNA or protein content, specific growth rate and time to perform DNA replication and cell division. On the other hand, existing predictive models are evaluated with respect to the newly developed theory. For the model of , a certain fitting parameter can also be related to physically meaningful parameters while for the model of [Augustin, J.-C., Rosso, L., Carlier, V.A. 2000. A model describing the effect of temperature history on lag time for Listeria monocytogenes. Int. J. Food Microbiol. 57, 169-181] a new, mechanistically based, model structure is proposed. A restriction of the proposed theory is that it is only valid for situations where biomass growth responds instantly to an environment change. The authors are aware of the fact that this assumption is not generally acceptable. Lag in biomass can be caused, for example, by a delayed synthesis of some essential growth factor (e.g., enzymes). In the second part of this series of papers [Dens, E.J., Bernaerts, K., Standaert, A.R., Kreft, J.-U., Van Impe, J.F., this issue. Cell division theory and individual-based modeling of microbial lag: part II. Modeling lag phenomena induced by temperature shifts. Int. J. Food Microbiol], the theory of cell division is implemented in an individual-based simulation program and extended to account for lags in biomass growth. In conclusion, the cell division theory applied to microbial populations in dynamic medium and/or temperature conditions provides a useful framework to analyze microbial lag behavior.