<p>Cloud and precipitation processes are still the main source of uncertainties in numerical weather prediction and climate change projections. The Priority Program "Polarimetric Radar Observations meet Atmospheric Modelling (PROM)", funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG), is guided by the hypothesis, that many uncertainties relate to the lack of observations suitable to challenge the representation of cloud and precipitation processes in atmospheric models. Such observations can, however, nowadays be provided e.g. by the recently installed dual-polarization C band weather radar network of the German national meteorological service in synergy with cloud radars and other instruments at German supersites and similar national networks increasingly available worldwide. While polarimetric radars potentially provide valuable in-cloud information e.g. on hydrometeor type, quantity, and microphysical cloud and precipitation processes, and atmospheric models employ increasingly higher moment microphysical modules, still considerable knowledge gaps exist in the interpretation of the observations and large uncertainties in the optimal microphysics model process formulations. PROM is a coordinated interdisciplinary effort to intensify the use of polarimetric radar observations in data assimilation, which requires a thorough evaluation and improvement of parametrizations of moist processes in atmospheric models. As an overview article of the inter-journal special issue "Fusion of radar polarimetry and numerical atmospheric modelling towards an improved understanding of cloud and precipitation processes", it outlines the knowledge achieved in PROM during the past two years and gives perspectives for the next four years.</p>