Electrochemical capacitors can store electrical energy harvested from intermittent sources and deliver energy quickly, but their energy density must be increased if they are to efficiently power flexible and wearable electronics, as well as larger equipment. This Review summarizes progress in the field of materials for electrochemical capacitors over the past decade as well as outlines key perspectives for future research. We describe electrical double-layer capacitors based on high-surface-area carbons, pseudocapacitive materials such as oxides and the two-dimensional inorganic compounds known as MXenes, and emerging microdevices for the Internet of Things. We show that new nanostructured electrode materials and matching electrolytes are required to maximize the amount of energy and speed of delivery, and different manufacturing methods will be needed to meet the requirements of the future generation of electronic devices. Scientifically justified metrics for testing, comparison and optimization of various kinds of electrochemical capacitors are provided and explained.