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<jats:p>Ten years ago, humidity observations were thought to give little benefit to global weather forecasts. Nowadays, at the European Centre for Medium‐range Weather Forecasts, satellite microwave radiances sensitive to humidity, cloud and precipitation provide 20% of short‐range forecast impact, as measured by adjoint‐based forecast sensitivity diagnostics. This makes them one of the most important sources of data and equivalent in impact to microwave temperature sounding observations. Forecasts of dynamical quantities, and precipitation, are improved out to at least day 6. This article reviews the impact of and the science behind these data. It is not straightforward to assimilate cloud and precipitation‐affected observations when the intrinsic predictability of cloud and precipitation features is limited. Assimilation systems must be able to operate in the presence of all‐pervasive cloud and precipitation ‘mislocation’ errors. However, by assimilating these observations using the ‘all‐sky’ approach, and supported by advances in data assimilation and forecast modelling, modern data assimilation systems can infer the dynamical state of the atmosphere, not just from traditional temperature‐related observations, but from observations of humidity, cloud and precipitation.</jats:p>