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The status of current efforts to assimilate cloud- and precipitation-affected satellite data is summarised with special focus on infrared and microwave radiance data obtained from operational Earth observation satellites. All global centres pursue efforts to enhance infrared radiance data usage due to the limited availability of temperature observations in cloudy regions where forecast skill is estimated to strongly depend on the initial conditions.Most systems focus on the sharpening of weighting functions at cloud top providing high vertical resolution temperature increments to the analysis, mainly in areas of persistent high and low cloud cover. Microwave radiance assimilation produces impact on the deeper atmospheric moisture structures as well as cloud microphysics and, through control variable and background-error formulation, also on temperature but to lesser extent than infrared data. Examples of how the impacts of these two observation types are combined are shown for subtropical low-level cloud regimes. The overall impact of assimilating such data on forecast skill is measurably positive despite the fact that the employed assimilation systems have been constructed and optimized for clear-sky data. This leads to the conclusion that a better understanding and modelling of model processes in cloud-affected areas and data assimilation system enhancements through inclusion of moist processes and their error characterization will contribute substantially to future forecast improvement.