Physics-informed neural networks (PINNs) have emerged as a novel framework that integrates physical laws with deep learning, demonstrating significant potential in recent geological reservoir studies. This approach offers an innovative pathway for addressing challenges in conventional reservoir research, such as high computational costs and heavy reliance on extensive data. The application progress of PINNs in various domains was systematically reviewed, including reservoir numerical simulation, parameter inversion, multiphase flow simulation, geothermal development, and CO₂ geological storage. By incorporating partial differential equations into the loss function of the neural network, PINNs enable high-precision predictions under data-sparse conditions while ensuring that solutions adhere to physical constraints. Results indicate that PINNs exhibit computational efficiency and mesh-free flexibility in areas such as surrogate model construction, history matching, and simulation of complex media. However, challenges remain, including high training costs and limited generalization capabilities. In the future, through algorithmic improvements, multi-source data integration, and hybridization with conventional methods, PINNs are expected to advance reservoir research toward more intelligent and efficient development.