Radiation is the one agent among all environmental factors which may damage biological systems that is not only easily quantifiable but can also be measured with unsurpassed resolution. Its primary effects on atoms and molecules are well understood, and the secondary processes can be followed by sophisticated experimental techniques. The quantum nature of interactions and the importance of stochastic variations call for an exact mathematical description. This task is by no means simple, and presents a challenge both to the experimentalist and to the theoretician. It is hoped that a generally acceptable formalism will help to quantify radiation responses, both in radiation protection and radiation therapy, and make it possible to move from a purely empirical approach with all its fallacies to real understanding.

Prelude: Why and to what end mathematical models In radiation biology

Models of cellular radiation action - an overview
Finestructures of energy deposition - introductory remarks
Analytics required by the multiple nature of radiation effects in cells
Problems in theoretical track structure research for heavy charged particles
Radiobiological modeling based on track structure
The role of energy distributions of charged particles in the mutagenic radiation action
Relative biological effectiveness: review of a model
Saturation in dual radiation action
Hit-size effectiveness approach in biophysical modeling
Interpreting survival observations using phenomenological models
Cluster theory of the effects of ionizing radiations
The LETHAL AND POTENTIALLY LETHAL model - a review and recent development
DNA double-strand breaks and their relation to cytoxicity
The pairwise lesion interaction model
A repair fixation model based on classical enzyme kinetics
Formal, empirical and mechanistic equations in cellular radiation biology.