Abstract: First-principles electronic structure calculations can accurately predict the physical and chemical properties of materials, and have become important research tools in physics, materials science, and chemistry. However, conventional first-principles methods are computationally demanding, which limits their applications in large-scale and high-throughput materials research. Recent advances in deep learning have created new opportunities for electronic structure calculations. This article introduces the background and fundamental concepts of deep learning applied to electronic structure analysis. Taking the deep learning Hamiltonian approach as a representative example, we focus on how interpretable neural-network models can be designed by incorporating important physical priors to achieve accurate predictions of electronic structures. We also review recent progress in emerging directions such as universal materials models for electronic structures and unsupervised learning. These developments suggest that artificial intelligence is driving first-principles calculations from conventional computational approaches toward a new paradigm jointly driven by data and physics, opening new avenues for future scientific computing and materials discovery.