Ocean temperature variability is a fundamental component of the Earth's climate system, and extremes in this variability affect the health of marine ecosystems around the world. The study of marine heatwaves has emerged as a rapidly growing field of research, given notable extreme warm-water events that have occurred against a background trend of global ocean warming. This review summarizes the latest physical and statistical understanding of marine heatwaves based on how they are identified, defined, characterized, and monitored through remotely sensed and in situ data sets. We describe the physical mechanisms that cause marine heatwaves, along with their global distribution, variability, and trends. Finally, we discuss current issues in this developing research area, including considerations related to thechoice of climatological baseline periods in defining extremes and how to communicate findings in the context of societal needs.