The magnitude and scale of global aerosol-cloud interactions and their influence on the anthropogenic radiative forcing remain key unanswered questions in atmospheric science. The aerosol-cloud mediated radiative forcing uncertainty has remained stubbornly high in global climate models throughout the IPCC reports, playing a major role in the overall uncertainty of anthropogenic climate forcing. The answers to these questions require deep understanding of aerosol and cloud distributions both in space and time, based on global observations that are practical only from satellites. The lack of significant advancement occurs despite the tremendous amount of data that is accumulating at an accelerating pace. This calls for innovative thinking about the fundamentals of these measurements and their relevance for quantifying aerosol-cloud interactions and their climatic effects. In particular, there is emerging evidence that the optical signature is frequently too weak to retrieve accurate cloud condensation nuclei (CCN) from atmospheric aerosol particles in the marine boundary layer. At low CCN concentrations, small variations in absolute concentration, indiscernible from satellites, constitute very large relative changes that may strongly affect cloud cover and albedo. Another obvious limitation is that cloud properties are determined by both aerosols and updrafts and, further, by mixing processes and by precipitation, but satellites generally constrain only the former. Further, standard remote-sensing retrievals provide cloud drop effective radius and optical depth (two extensive quantities that are dependent on cloud liquid- or ice water path), whereas what is needed are cloud particle concentrations (droplets or ice crystals) and water path. There is therefore an urgent need to evaluate the quality and limitations of the available datasets and propose new approaches of analyses of the existing data. In particular, techniques to develop simultaneous aerosol and cloud retrieval algorithms for global observations are urgently needed. Essential remaining gaps will be identified and addressed by recommending new satellite missions targeted at filling these gaps. The proposed ISSI team aims to solidify our understanding of these issues and make substantial progress towards quantifying the strength of aerosol-cloud interactions and their associated radiative forcing.