Over the last five decades, Earth's atmosphere has been extensively monitored from space using different spectral ranges. Early efforts were directed at improving weather forecasts with the first meteorological satellites launched in the 1960s. Soon thereafter, the intersection between weather, climate and atmospheric chemistry led to the observation of atmospheric composition from space. During the 1970s the Nimbus satellite program started regular monitoring of ozone integrated columns and water vapor profiles using the Backscatter Ultraviolet Spectrometer, the Infrared Interferometer Spectrometer and the Satellite Infrared Spectrometer instruments. Five decades after these pioneer efforts, continuous progress in instrument design, and retrieval techniques allow researchers to monitor tropospheric concentrations of a wide range of species with implications for air quality, climate and weather. The time line of historic, present and future space-borne instruments measuring ultraviolet and visible backscattered solar radiation designed to quantify atmospheric trace gases is presented. We describe the instruments technological evolution and the basic concepts of retrieval theory. We include a review of algorithms developed for ozone, nitrogen dioxide, sulfur dioxide, formaldehyde, bromine monoxide, water vapor and glyoxal, a selection of studies using these algorithms, the challenges they face and how these challenges can be addressed. The paper ends by providing insights on the opportunities that new instruments will bring to the atmospheric chemistry, weather and air quality communities and how to address the pressing need for long-term, inter-calibrated data records necessary to monitor the response of the atmosphere to rapidly changing ecosystems.