Critical aspects of computational imaging systems, such as experimental design and image priors, can be optimized through deep networks formed by the unrolled iterations of classical physics-based reconstructions. Termed physics-based networks, they incorporate both the known physics of the system via its forward model, and the power of deep learning via data-driven training. However, for realistic large-scale physics-based networks, computing gradients via backpropagation is infeasible due to the memory limitations of graphics processing units. In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network's layers to enable physics-based learning for large-scale computational imaging systems. We demonstrate our method on a compressed sensing example, as well as two large-scale real-world systems: 3D multi-channel magnetic resonance imaging and super-resolution optical microscopy.