Multibody dynamics simulation of the musculoskeletal system is an essential tool for analyzing the biomechanical mechanisms underlying human motion. Recent research trends have shifted from traditional physics-based models toward data-driven or data-physics hybrid frameworks. This review presents the latest developments in these areas. Physics-based multibody dynamics simulations have undergone significant progress in terms of simulation fidelity, optimization algorithms, and software tools. However, their practical implementation remains constrained by the need for complex experimental data and the computational expense of solving differential equations. Conversely, data-driven methods bolstered by advancements in deep learning have demonstrated remarkable efficiency in predicting joint angles, postures, ground reaction forces, joint torques, and muscle forces, as well as developing control algorithms for exoskeletons. However, despite these advantages, data-driven approaches face challenges such as limited generalizability and potential violation of biomechanical principles.To address these limitations, data-physics hybrid approaches (e.g., physics-informed neural network, PINN) which integrate physical constraints (e.g., Newton-Euler equations, muscle constitutive laws) with data-driven architectures have been developed. This synergy enhances prediction accuracy while preserving the biological plausibility of solutions. Nevertheless, critical challenges persist, including the integration of multi-scale physical equations and the modeling of multi-joint coordination dynamics. Future research should prioritize: optimizing hybrid model architectures to balance computational efficiency and mechanistic accuracy, incorporating markerless motion capture techniques to improve real-world applicability, exploiting multi-scale physics and personalized parameter inversion to advance precision rehabilitation and motion analysis. These efforts will foster innovations in intelligent rehabilitation systems, clinical motion assessment, and related translational fields.