This article reviews atmospheric changes associated with 44 solar eclipses, beginning with the first quantitative results available, from 1834 (earlier qualitative accounts also exist). Eclipse meteorology attracted relatively few publications until the total solar eclipse of 16 February 1980, with the 11 August 1999 eclipse producing the most papers. Eclipses passing over populated areas such as Europe, China and India now regularly attract scientific attention, whereas atmospheric measurements of eclipses at remote locations remain rare. Many measurements and models have been used to exploit the uniquely predictable solar forcing provided by an eclipse. In this paper, we compile the available publications and review a subset of them chosen on the basis of importance and novelty. Beyond the obvious reduction in incoming solar radiation, atmospheric cooling from eclipses can induce dynamical changes. Observations and meteorological modelling provide evidence for the generation of a local eclipse circulation that may be the origin of the ‘eclipse wind’. Gravity waves set up by the eclipse can, in principle, be detected as atmospheric pressure fluctuations, though theoretical predictions are limited, and many of the data are inconclusive. Eclipse events providing important early insights into the ionization of the upper atmosphere are also briefly reviewed. This article is part of the themed issue ‘Atmospheric effects of solar eclipses stimulated by the 2015 UK eclipse’.