Thermal remote sensing is widely used in the detection, study, and management of biomass burning occurring in open vegetation fires. Such fires may be planned for land management purposes, may occur as a result of a malicious or accidental ignition by humans, or may result from lightning or other natural phenomena. Under suitable conditions, fires may spread rapidly and extensively, affecting the land cover properties of large areas, and releasing a wide variety of gases and particulates directly into Earth’s troposphere. On average, around 3.4 % of the Earth’s terrestrially vegetated area burns annually in this way. Vegetation fires inevitably involve high temperatures, so thermal remote sensing is well suited to its identification and study. Here we review the theoretical basis of the key approaches used to (1) detect actively burning fires; (2) characterize sub-pixel fires; and (3) estimate fuel consumption and smoke emissions. We describe the types of airborne and spaceborne systems that deliver data for use with these active fire thermal remote sensing methods, and provide some examples of how operational fire management and fire research have both benefited from the resulting information. We commence with a brief review of the significance and magnitude of biomass burning, both within the ‘whole Earth’ system and in more regional situations, aiming to highlight why thermal remote sensing has become so important to the study and management of open vegetation burning.