Five decades observing Earth’s atmospheric trace gases using ultraviolet and visible backscatter solar radiation from space

•Review of nadir UV–vis space-borne instruments for monitoring of atmospheric composition.•Description of trace gase retrieval techniques in the UV–vis spectral range.•Summary of ozone, nitrogen dioxide, sulfur dioxide, formaldehyde, bromine monoxide, water vapor and glyoxal retrievals developed since 1970.•Illustration of the scientific and societal applications of these retrievals.•Recommendations and challenges in the following decade.