Physics-guided deep learning (PGDL) integrates physical principles with data-driven methods to better model complex dynamical systems. Traditional physics-based models are explainable and efficient but require strong assumptions and are computationally intensive. Deep learning (DL) offers flexibility and speed but lacks physical reasoning and interpretability. PGDL combines the strengths of both, enabling accurate, interpretable, and generalizable models. It addresses challenges in learning dynamical systems from data, including high-dimensional, non-stationary, and uncertain dynamics. PGDL uses physical constraints to guide learning, improving generalization and reducing sample complexity. It has applications in scientific simulation, equation discovery, and dynamics forecasting. Key approaches include residual models, trainable operators, equivariant learning, and disentangled representations. Challenges remain in ensuring stability, robustness, uncertainty quantification, non-Euclidean geometry, explainability, and theoretical guarantees. Future research aims to enhance PGDL's ability to handle complex physical systems, improve model interpretability, and develop trustworthy AI models for scientific discovery.Physics-guided deep learning (PGDL) integrates physical principles with data-driven methods to better model complex dynamical systems. Traditional physics-based models are explainable and efficient but require strong assumptions and are computationally intensive. Deep learning (DL) offers flexibility and speed but lacks physical reasoning and interpretability. PGDL combines the strengths of both, enabling accurate, interpretable, and generalizable models. It addresses challenges in learning dynamical systems from data, including high-dimensional, non-stationary, and uncertain dynamics. PGDL uses physical constraints to guide learning, improving generalization and reducing sample complexity. It has applications in scientific simulation, equation discovery, and dynamics forecasting. Key approaches include residual models, trainable operators, equivariant learning, and disentangled representations. Challenges remain in ensuring stability, robustness, uncertainty quantification, non-Euclidean geometry, explainability, and theoretical guarantees. Future research aims to enhance PGDL's ability to handle complex physical systems, improve model interpretability, and develop trustworthy AI models for scientific discovery.