Modern experimental techniques now reveal the structure and function of neural circuits at unprecedented scale and resolution. How can we use this wealth of data to understand how cells and circuits implement computations underlying behaviour? Achieving this goal requires models that are consistent with biophysical mechanisms and circuit dynamics, yet flexible enough to capture behaviourally relevant computations. We develop simulation-based machine learning methods that address this challenge. I will show how these approaches—in combination with connectomic measurements—make it possible to build large-scale mechanistic models of the fruit fly visual system. Our methods generalize across systems and scales, defining a new way to study biological systems by algorithmically learning interpretable models that reveal how structure and dynamics gives rise to behaviour.