Insects constitute the most species-rich radiation of metazoa, a success that is due to the evolution of active flight. Unlike pterosaurs, birds and bats, the wings of insects did not evolve from legs1, but are novel structures that are attached to the body via a biomechanically complex hinge that transforms tiny, high-frequency oscillations of specialized power muscles into the sweeping back-and-forth motion of the wings2. The hinge consists of a system of tiny, hardened structures called sclerites that are interconnected to one another via flexible joints and regulated by the activity of specialized control muscles. Here we imaged the activity of these muscles in a fly using a genetically encoded calcium indicator, while simultaneously tracking the three-dimensional motion of the wings with high-speed cameras. Using machine learning, we created a convolutional neural network3 that accurately predicts wing motion from the activity of the steering muscles, and an encoder–decoder4 that predicts the role of the individual sclerites on wing motion. By replaying patterns of wing motion on a dynamically scaled robotic fly, we quantified the effects of steering muscle activity on aerodynamic forces. A physics-based simulation incorporating our hinge model generates flight manoeuvres that are remarkably similar to those of free-flying flies. This integrative, multi-disciplinary approach reveals the mechanical control logic of the insect wing hinge, arguably among the most sophisticated and evolutionarily important skeletal structures in the natural world. Measurements of fly muscle activity using a genetically encoded calcium indicator and high-speed imaging of wing movement were used to construct a model of the insect wing hinge and the role of steering muscles in flight control.