Abstract
A summary of the key aspects of radiobiological modelling is provided, based on the theoretical and practical concepts of the linear quadratic model, which gradually replaced other numerical approaches. The closely related biological effective dose concept is useful in many clinical applications. Biological effective dose formulations in conventional photon-based radiotherapy continue to be developed, and can be extended to the now increasingly used proton and ion-beam therapy, to very low or high dose ranges, the dose rate effect, hypoxia and repopulation. Such established and new research developments will be of interest to clinicians, physicists and biologists to better understand the processes underlying radiotherapy and assist their collaborative efforts to make radiotherapy safer and more effective.