Since Johnson's experimental observations of thermal noise in 1927, and Nyquist's explanation of the phenomenon shortly afterwards in 1928, thermal noise has attracted interest as a means of measuring temperature. The independence of the thermal noise from the material nature of the sensor makes it particularly attractive for metrological applications. However, the noise signals are extremely small and some ingenuity is required to make accurate measurements. This paper reviews the foundations of Johnson noise thermometry and the various techniques that have been employed to measure temperature via Johnson noise. Emphasis is placed on key developments in noise thermometers for metrological applications. The review includes the current activities of teams involved in noise thermometry research.