Over the past two decades, there has been a growing interest in the use of plasmonic nanoparticles as sources of heat remotely controlled by light, giving rise to the field of thermoplasmonics. The ability to release heat on the nanoscale has already impacted a broad range of research activities, from biomedicine to imaging and catalysis. Thermoplasmonics is now entering an important phase: some applications have engaged in an industrial stage, while others, originally full of promise, experience some difficulty in reaching their potential. Meanwhile, innovative fundamental areas of research are being developed. In this Review, we scrutinize the current research landscape in thermoplasmonics, with a specific focus on its applications and main challenges in many different fields of science, including nanomedicine, cell biology, photothermal and hot-electron chemistry, solar light harvesting, soft matter and nanofluidics.