Models of cognitive processes often include simplifications, idealisations, and fictionalisations, so how should we learn about cognitive processes from such models? Particularly in cognitive science, when many features of the target system are unknown, it is not always clear which simplifications, idealisations, and so on, are appropriate for a research question, and which are highly misleading. Here we use a case-study from studies of language evolution, and ideas from philosophy of science, to illustrate a robustness approach to learning from models. Robust properties are those that arise across a range of models, simulations and experiments, and can be used to identify key causal structures in the models, and the phenomenon, under investigation. For example, in studies of language evolution, the emergence of compositional structure is a robust property across models, simulations and experiments of cultural transmission, but only under pressures for learnability and expressivity. This arguably illustrates the principles underlying real cases of language evolution. We provide an outline of the robustness approach, including its limitations, and suggest that this methodology can be productively used throughout cognitive science. Perhaps of most importance, it suggests that different modelling frameworks should be used as tools to identify the abstract properties of a system, rather than being definitive expressions of theories.