Inverse problems address the problem of identifying models from data. The models to be identified may be differential equations, and the data may be solutions of the differential equations, which are obtained through observations. Inverse problems often require innovative approaches for accurate solutions. This chapter introduces deep learning-based methods for inverse problems, including physics-informed neural networks, iterative forward solvers (adapted from adjoint optimization), and data-driven approaches. Applications in nondestructive testing and topology optimization highlight the practical utility of these techniques. The discussions are aimed at equipping researchers with tools to address complex, data-constrained engineering challenges in model discovery.