Considerable attention has been directed at understanding the consequences and impacts of long-term anthropogenic climate change. Discrete, climatically extreme events such as cyclones, floods, and heatwaves can also significantly affect regional environments and species, including humans. Climate change is expected to intensify these events and thus exacerbate their effects. Climatic extremes also occur in the ocean, and recent decades have seen many high-impact marine heatwaves (MHWs)—anomalously warm water events that may last many months and extend over thousands of square kilometers. A range of biological, economic, and political impacts have been associated with the more intense MHWs, and measuring the severity of these phenomena is becoming more important. Progress in understanding and public awareness will be facilitated by consistent description of these events. Here, we propose a detailed categorization scheme for MHWs that builds on a recently published classification, combining elements from schemes that describe atmospheric heatwaves and hurricanes. Category I, II, III, and IV MHWs are defined based on the degree to which temperatures exceed the local climatology and illustrated for 10 MHWs. While there is a long-term increase in the occurrence frequency of all MHW categories, the largest trend is a 24% increase in the area of the ocean where strong (Category II) MHWs occur. Use of this scheme can help explain why biological impacts associated with different MHWs can vary widely and provides a consistent way to compare events. We also propose a simple naming convention based on geography and year that would further enhance scientific and public awareness of these marine events.