The modeling and simulation of polymer systems present unique challenges due to their intrinsic complexity and multi-scale behavior. Traditional computational methods, while effective, often struggle to balance accuracy with computational efficiency, especially when bridging the atomistic to macroscopic scales. Recently, physics-informed neural networks (PINNs) have emerged as a promising tool that integrates data-driven learning with the governing physical laws of the system. This review discusses the development and application of PINNs in the context of polymer science. It summarizes the recent advances, outlines the key methodologies, and analyzes the benefits and limitations of using PINNs for polymer property prediction, structural design, and process optimization. Finally, it identifies the current challenges and future research directions to further leverage PINNs for advanced polymer modeling.