A grand challenge in climate science is to translate advances in our fundamental understanding into reduced uncertainty in climate projections Model uncertainty, characterized for example by the spread of simulations of future climate projections, has changed little over the past few decades despite major advances in model complexity, resolution, and the growing number of intercomparison projects and observational datasets. Here we argue that the use of perturbed parameter ensembles (PPEs) would accelerate our understanding of uncertainty in its broadest sense and help identify strategies for reducing it. We make eleven recommendations for future research priorities, drawing on existing studies that use PPEs to guide model development and simplification, understand inter-model differences, more fully characterize the plausible spread in climate projections, formalize model calibration, define observational requirements, and investigate how interacting environmental conditions influence complex climate systems like cloud fields. These studies extend across climate, weather, atmospheric chemistry, clouds, aerosols and renewable energy using process-based high-resolution models through to global-scale models. Although increases in model complexity, resolution and intercomparison projects consume most computing resources today, we argue that, in synergy with these efforts, PPEs are essential for fully characterizing model uncertainty and improving model reliability, and that they should be prioritized when allocating those resources.