Space-borne remote sensing of atmospheric chemical constituents is crucial for monitoring and better understanding global and regional air quality. Since the 1990s, the continuous development of instruments onboard low-Earth orbiting (LEO) satellites has led to major advances in air quality research by providing daily global measurements of atmospheric chemical species. The next generation of atmospheric composition satellites measures from the geostationary Earth orbit (GEO) with hourly temporal resolution, allowing the observation of diurnal variations of air pollutants. The first two instruments of the GEO constellation coordinated by the Committee on Earth Observation Satellites (CEOS), the Geostationary Environment Monitoring Spectrometer (GEMS) for Asia and the Tropospheric Emissions: Monitoring of Pollution (TEMPO) for North America, were successfully launched in 2020 and 2023, respectively. The European component, Sentinel-4, is planned for launch in 2025. This work provides an overview of satellite missions for atmospheric composition monitoring and the state of the science in air quality research. We cover recent advances in retrieval algorithms, the modeling of emissions and atmospheric chemistry, data assimilation, and the application of machine learning based on satellite data. We discuss the challenges and opportunities in air quality research in the era of GEO satellites and provide recommendations on research priorities for the near future.