Experimental techniques now make it possible to measure the structure and function of neural circuits at an unprecedented scale and resolution. How can we leverage this wealth of data to understand how neural circuits perform computations underlying behaviour? A mechanistic understanding will require models that align with experimental measurements and biophysical mechanisms, while also being capable of performing behaviorally relevant computations. Building such models has remained a central challenge. I will present our work on addressing this challenge. We have developed machine learning methods and differentiable simulators that make it possible to algorithmically identify models that link biophysical mechanisms, neural data, and behaviour. I will show how these approaches—in combination with modern connectomic measurements—make it possible to build large-scale mechanistic models of the fruit fly visual system, and how such a model can make experimentally testable predictions for each neuron in the system. Our approach combines probabilistic machine learning with the simulation of neural dynamics, presenting a general strategy for building, interpreting, and updating large-scale mechanistic models, yielding insights into the neural mechanisms underlying behaviour.