In April 2017, the Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) established the Priority Programme “Polarimetric Radar Observations meet Atmospheric Modelling (PROM)” (SPP 2115). The programme is designed to run for 6 years and is now in the third funding year. The overall motivation of the SPP PROM is a better understanding and representation of cloud and precipitation processes in numerical weather prediction and climate models. Since 2015 the whole atmosphere over Germany has been monitored by 17 state-of-the-art polarimetric Doppler weather radar observations suitable to challenge the representation of cloud and precipitation processes in atmospheric models. Data assimilation merges observations and models for state estimation as a prerequisite for prediction and can be regarded as a smart interpolation between observations while exploiting the physical consistency of atmospheric models as mathematical constraints. However, considerable knowledge gaps exist both in radar polarimetry and atmospheric models, which impede the full exploitation of the triangle radar-polarimetry–atmospheric-models–data-assimilation. Objectives of SPP PROM and thus the envisioned publications within the special issue are (1) the exploitation of radar polarimetry for quantitative process detection in precipitating clouds and for model evaluation, (2) the improvement of cloud and precipitation schemes in atmospheric models based on process fingerprints detectable in polarimetric observations, (3) monitoring of the energy budget evolution due to phase changes in the cloudy, precipitating atmosphere for a better understanding of its dynamics, (4) the generation of precipitation system analyses by the assimilation of polarimetric radar observations into atmospheric models for weather forecasting, and (5) radar-based detection of the initiation of convection for the improvement of thunderstorm prediction.