A review is given of developments in the theory and application of the quantum statistics of visible-light photons, particularly of scattered laser light, over the fifty years since Maiman’s publication of the first working laser. Some introductory pre-laser historical background to photon statistics is included and details are given of research and commercial developments in the field conducted in the author’s laboratory in the UK over the period. The resulting emergence of photon statistics and photon-correlation spectroscopy as widely used techniques for non-invasive measurements of diffusion and velocity in many present-day areas of science and industry is described.