The past twenty-five years have seen an unparalleled increase in understanding of cancer biology. Over this period, mathematical modelling has emerged as a powerfull tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testing hypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving cancer treatment.

In this talk, I will focus on modelling approaches that have been used to investigate solid tumour growth and response to radiotherapy. The models will range from simple, phenomenological models that view the tumour as a homogeneous mass, to more detailed models that resolve the subcellular dynamics of the cell cycle and describe how these dynamics are impacted by fluctuations in oxygen levels, and finally multiscale models that can be used to understand how interactions between subcellular, cellular and tissue scale processes impact a tumour’s overall growth dynamics and its response to radiotherapy.