Physics-informed neural networks (PINNs) integrate physics-based models with data to solve fluid mechanics problems. This review discusses the application of PINNs in various fluid dynamics scenarios, including incompressible, compressible, and biomedical flows. PINNs use neural networks to approximate solutions to partial differential equations (PDEs) by incorporating physical laws into the loss function. This approach allows for the seamless integration of data and mathematical models, enabling the solution of inverse problems where parameters or boundary conditions are unknown. PINNs are particularly effective when sparse data are available, as they can accurately infer flow fields without requiring a mesh. The review highlights the use of PINNs in reconstructing 3D wake flows, supersonic flows, and biomedical flows, demonstrating their ability to handle complex, high-dimensional problems. PINNs are also applied to compressible flows, where they infer density, pressure, and velocity fields using limited data. In biomedical flows, PINNs are used to infer material properties of thrombi based on phase field data. The review emphasizes the potential of PINNs as a complementary approach to traditional CFD methods, offering a flexible and efficient framework for solving fluid mechanics problems with available data. The effectiveness of PINNs is demonstrated through various case studies, showing their ability to accurately predict flow fields and material properties in complex scenarios.Physics-informed neural networks (PINNs) integrate physics-based models with data to solve fluid mechanics problems. This review discusses the application of PINNs in various fluid dynamics scenarios, including incompressible, compressible, and biomedical flows. PINNs use neural networks to approximate solutions to partial differential equations (PDEs) by incorporating physical laws into the loss function. This approach allows for the seamless integration of data and mathematical models, enabling the solution of inverse problems where parameters or boundary conditions are unknown. PINNs are particularly effective when sparse data are available, as they can accurately infer flow fields without requiring a mesh. The review highlights the use of PINNs in reconstructing 3D wake flows, supersonic flows, and biomedical flows, demonstrating their ability to handle complex, high-dimensional problems. PINNs are also applied to compressible flows, where they infer density, pressure, and velocity fields using limited data. In biomedical flows, PINNs are used to infer material properties of thrombi based on phase field data. The review emphasizes the potential of PINNs as a complementary approach to traditional CFD methods, offering a flexible and efficient framework for solving fluid mechanics problems with available data. The effectiveness of PINNs is demonstrated through various case studies, showing their ability to accurately predict flow fields and material properties in complex scenarios.