<p><?tk 4?>Physics-informed neural networks (PINNs) offer a transformative alternative to conventional computational fluid dynamics (CFD) by embedding governing physical laws directly into neural network loss functions. While traditional CFD methods face limitations including high computational costs, mesh sensitivity, and extensive data requirements, PINNs overcome these barriers by ensuring solutions inherently satisfy conservation principles during training. This review examines PINN foundations and their dual capability in solving forward problems—predicting complex fluid behaviors—and inverse problems involving parameter identification from limited data. We categorize existing research across three dimensions: canonical flows (Couette, Poiseuille), constitutive models (non-Newtonian, viscoelastic), and mathematical formulations (Burgers, Cahn-Hilliard equations). Building on this framework, we discuss advanced PINN variants addressing limitations in accuracy, efficiency, and generalization. We conclude by outlining future directions in multiscale modeling, irregular geometries, and data-driven discovery of constitutive laws, highlighting PINNs’ potential to revolutionize computational strategies for complex fluids.</p> Graphical abstract <p></p>