Normal tissue responses to ionizing radiation have been a major subject for study since the discovery of X-rays at the end of the 19th century. Shortly thereafter, time-dose relationships were established for some normal tissue endpoints that led to investigations into how the size of dose per fraction and the quality of radiation affected outcome. The assessment of the radiosensitivity of bone marrow stem cells using colony-forming assays by Till and McCulloch prompted the establishment of in situ clonogenic assays for other tissues that added to the radiobiology toolbox. These clonogenic and functional endpoints enabled mathematical modeling to be performed that elucidated how tissue structure, and in particular turnover time, impacted clinically relevant fractionated radiation schedules. More recently, lineage tracing technology, advanced imaging and single cell sequencing have shed further light on the behavior of cells within stem, and other, cellular compartments, both in homeostasis and after radiation damage. The discovery of heterogeneity within the stem cell compartment and plasticity in response to injury have added new dimensions to the consideration of radiation-induced tissue damage. Clinically, radiobiology of the 20th century garnered wisdom relevant to photon treatments delivered to a fairly wide field at around 2 Gy per fraction, 5 days per week, for 5-7 weeks. Recently, the scope of radiobiology has been extended by advances in technology, imaging and computing, as well as by the use of charged particles. These allow radiation to be delivered more precisely to tumors while minimizing the amount of normal tissue receiving high doses. One result has been an increase in the use of schedules with higher doses per fraction given in a shorter time frame (hypofractionation). We are unable to cover these new technologies in detail in this review, just as we must omit low-dose stochastic effects, and many aspects of dose, dose rate and radiation quality. We argue that structural diversity and plasticity within tissue compartments provides a general context for discussion of most radiation responses, while acknowledging many omissions. © 2020 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland.