Among the great variety of temperature-measurement techniques, radiation thermometry has a unique potential. As an optical contactless method, it allows remote sensing of the object temperature without influencing it, measurements of rapidly moving objects, and measurements of very high temperatures. Its high flexibility, its great accuracy potential, and the possibility of accurately tracing the measurement back to the International Temperature Scale (ITS) have made radiation thermometry a method widely used in science, industry, medicine, and everyday life. Traceability of temperature measurements is of increasing importance, as further globalisation will require comparability of temperature measurement world-wide. This can be ensured only if the measurement can be traced back to the ITS, which means that the result of a measurement can be related to stated references of the ITS through an unbroken chain of comparisons, all of them with stated uncertainties. The Physikalisch-Technische Bundesanstalt (PTB), the National Metrology Institute of Germany, maintains, provides, and further develops a wide range of instrumentation for radiation-temperature measurements, allowing temperature measurements to be carried out from -60°C to 3000 °C which are directly traceable to the ITS. After an introduction to the International Temperature Scale of 1990 (ITS-90) and a brief outline of PTB's history of thermal-radiation measurements, this article describes the present state of the art of high-accuracy radiation thermometry reached and further developed at PTB. The article deals with different temperature ranges requiring different measurement and traceability techniques. In modern radiation thermometry, heat-pipe blackbodies combined with platinum resistance thermometers and radiation thermometers equipped with photodetectors for infrared radiation are applied in the temperature range from -60°C to 961.78°C (the freezing temperature of silver). Within the scope of the European research project TRIRAT (traceability in infrared-radiation thermometry), significant progress could be achieved in traceable low-temperature radiation thermometry. This progress and recent developments aiming to extend the measurements to temperatures below -60 °C are summarised. Novel developments in high-temperature radiation thermometry from 962°C to 3000°C. which are required by the semiconductor, steel, and glass industry in particular, are dealt with in a separate section. The calibration capabilities of the PTB in this temperature range are described, and the European project HIMERT (novel high-temperature metal-carbon eutectic fixed points for radiation thermometry, radiometry, and thermocouples) is presented. In this project, considerable effort is made on the international level to further improve the high-temperature scale by developing and characterising advanced fixed-point materials. Independently of radiation-thermometric methods, which need defined temperature fixed points, the PTB performs direct measurements of the thermodynamic temperature by applying radiation detectors calibrated in absolute terms for their spectral responsivity. This radiometric method is used to further improve the ITS and might contribute to a future re-definition of the temperature unit kelvin. It is described in the last section of this review and recent results regarding the agreement between thermodynamic temperature and the ITS are given.