Ocean colour remote sensing from sun-synchronous polar orbiting satellites has become well-established as a tool for extracting information on phytoplankton and suspended particulate matter and related processes in regional seas. New data is now becoming available from optical remote sensors on geostationary satellites and provides a much higher temporal resolution, typically an image once or more per hour during daylight compared to once per day. This higher temporal resolution opens up obvious opportunities for dramatically improving the data availability in periods of scattered clouds and for resolving fast processes such as tidal or diurnal variability of phytoplankton or suspended particulate matter. As the science community starts to explore this new data source, further new applications are likely to emerge. However, the geostationary orbit presents also new algorithmic challenges. The coverage of high latitudes is limited by the difficulties of atmospheric correction at very high sensor zenith angle and ultimately by the earth's curvature. Exploitation of the new possibilities of viewing the earth for a range of sun zenith angles over the day also stimulates a need to perform accurate atmospheric correction at high sun zenith angle. Traditional pixel-by-pixel data processing algorithms could be supplemented by information on the temporal coherency of data over the day thus potentially improving data quality, by adding constraints to the inversion problem, or data quality control, by a posteriori analysis of time series. This review assesses the challenges and opportunities of geostationary ocean colour, with emphasis on the data processing algorithms that will need to be improved or developed to fully exploit the potential of this data source. Examples are drawn from recent results using data from the GOCI and SEVIRI sensors.