Photon avalanche (PA)-where the absorption of a single photon initiates a 'chain reaction' of additional absorption and energy transfer events within a material-is a highly nonlinear optical process that results in upconverted light emission with an exceptionally steep dependence on the illumination intensity. Over 40 years following the first demonstration of photon avalanche emission in lanthanide-doped bulk crystals, PA emission has been achieved in nanometer-scale colloidal particles. The scaling of PA to nanomaterials has resulted in significant and rapid advances, such as luminescence imaging beyond the diffraction limit of light, optical thermometry and force sensing with (sub)micron spatial resolution, and all-optical data storage and processing. In this review, we discuss the fundamental principles underpinning PA and survey the studies leading to the development of nanoscale PA. Finally, we offer a perspective on how this knowledge can be used for the development of next-generation PA nanomaterials optimized for a broad range of applications, including mid-IR imaging, luminescence thermometry, (bio)sensing, optical data processing and nanophotonics.