Uncertainty in estimations of the net contribution of anthropogenic aerosol particles, particularly of aerosol-cloud interactions (ACIs) to the Earth’s radiation budget, limits our ability to understand past and project future climate change. Earth System Models (ESMs) are among the key tools for assessing the magnitude and impacts of changes in various forcing agents on the global climate system. Hence, improving aerosol and cloud descriptions in ESMs is an important way forward to increase the confidence in estimates of climate impacts of aerosol perturbations in the past, present and future. In the framework of the FORCeS project, experimental and theoretical approaches were combined to bridge the current key gaps in the fundamental understanding of essential aerosol and cloud processes and their descriptions in selected European ESMs. Regarding aerosol types and processes, we focused on organic aerosol, particulate nitrate, absorbing aerosols, and ultrafine aerosol sources including new particle formation and growth. In terms of cloud processes, we targeted cloud droplet activation, hydrometeor growth and evaporation, ice formation and multiplication as well as aerosol processing and scavenging by clouds. The selection was made based on the identified knowledge gaps in the scientific understanding of these processes and/or their current representation in ESMs, as well as a novel perturbed parameter ensemble approach to detecting potential structural deficiencies in an ESM. Here, we review the state-of-the-art, outline our approach for arriving at recommendations for improving the representation of key aerosol and cloud processes within ESMs, and then provide such recommendations applicable in models operating at the Earth system scale. The limitations of the recommendations, applicability, as well as alternative approaches and future research directions are discussed. Overall, the findings highlight the need for continuous efforts towards smart ways for representing the aerosol number size distribution as well as consistent representations of key parameters (e.g., liquid water content and cloud droplet number concentration). Furthermore, we provide guidance for future ESM evaluation emphasising, in particular, the need for exploring the consistency of key parameters, process-based (as opposed to parameter-based), and the complementarity of in-situ and remote-sensed measurements for model evaluation.