FLASH radiotherapy (FLASH-RT) is a technology that could modify the way radiotherapy is delivered in the future. This technique involves the ultra-fast delivery of radiotherapy at dose rates several orders of magnitude higher than those currently used in routine clinical practice. This very short time of exposure leads to the striking observation of relative protection of normal tissues that are exposed to FLASH-RT as compared with conventional dose rate radiotherapy. Here we summarise the current knowledge about the FLASH effect and provide a synthesis of the observations that have been reported on various experimental animal models (mice, zebrafish, pig, cats), various organs (lung, gut, brain, skin) and by various groups across 40 years of research. We also propose possible mechanisms for the FLASH effect, as well as possible paths for clinical application.