The 2010 eruption of Eyjafjallajökull volcano in Iceland changed the rules for air travel in Europe and introduced the use of restricted fly zones based on ash-cloud concentrations calculated by dispersion models. This change prompted a sustained effort to improve the accuracy of ash-cloud model forecasts. In this paper we describe how this goal is being advanced on three fronts: (1) assessing current capabilities and establishing best practices; (2) improving the accuracy of model inputs; and (3) developing strategies to automatically compare model output with observations and adjust inputs to produce the best match. Progress has been made on all three fronts. A key lesson is that accuracy can only be quantified by comparison with reliable observations, which are often elusive. Model improvements will have to be made in tandem with new technologies to observe and measure.