Johnson noise thermometers infer thermodynamic temperature from measurements of the thermally-induced current fluctuations that occur in all electrical conductors. This paper reviews the status of Johnson noise thermometry and its prospects for both metrological measurements and for practical applications in industry. The review begins with a brief description of the foundations and principles of Johnson noise thermometry before outlining the many different techniques and technological breakthroughs that have enabled the application of Johnson noise thermometry to high-accuracy, cryogenic, and industrial thermometry. Finally, the future of noise thermometry is considered. As the only purely electronic approach to thermodynamic temperature measurement, Johnson noise thermometry has appeal for metrological applications at temperatures ranging from below 1 mK up to 800 K. With the rapid advances in digital technologies, there are also expectations that noise thermometry will become a practical option for some industrial applications, perhaps reaching temperatures above 2000 K.