Several mathematical and statistical approaches are established in radiation oncology, including the widely used Linear Quadratic (LQ) model, Biologically Effective Dose (BED), Tumor Control Probability (TCP), and Normal Tissue Complication Probability (NTCP) models. More recently, mechanistic mathematical models (including ordinary and partial differential equations) have been developed to simulate the nonlinear dynamics during radiation therapy. Mathematical models, calibrated and validated on historic clinical data, have demonstrated remarkable success in identifying innovative treatment protocols that have been subsequently validated in clinical trials in a variety of cancers and treatments. In this lecture, I will introduce the concepts of mathematical modeling and computer simulation for radiobiology and radiation biology. I will summarize cross-disciplinary modeling breakthroughs, and use individual studies to demonstrate the power of such data-driven models to guide clinical decision making, including personalizing radiation dose, dose fractionation, and organ-at-risk sparing. I will demonstrate how such models can help develop digital twins and in silico trials to learn how to best deploy radiation to individual patients.