We present a review of the use of gamma ray spectrometry as a diagnostic of nuclear reaction rates and nuclear reaction product densities in high temperature fusion plasmas. In this review we will discuss the historic genesis of the concept, a brief overview of the relevant nuclear physics, the experimental techniques utilised in the measurements and some of the analytical techniques required to extract the diagnostic information from the basic measurements. Of particular interest is the ability to measure the population of confined fast alpha particles in future burning plasma experiments.