The strong non-linearity and multi-scale coupling characteristics of massive heterogeneous components in modern power systems pose severe challenges to traditional numerical simulation methods, rendering them inadequate for urgent online real-time assessment. This paper systematically reviews state-of-the-art hybrid transient stability simulation technologies that deeply integrate physics and data. It first dissects the critical bottlenecks of traditional numerical simulations—specifically computational inefficiency, convergence fragility, and model fidelity gaps—to elucidate the necessity of evolving toward a new physics–data integration paradigm. Subsequently, the review categorizes current methodologies into three technical dimensions: artificial intelligence (AI)-enhanced numerical solvers, AI-based surrogate modeling, and physics-embedded AI modeling. These approaches are synthesized to demonstrate their unique advantages in breaking through computational speed limits, enhancing numerical robustness, and effectively bridging the fidelity gap between simulation models and physical reality. Finally, addressing existing limitations regarding physical consistency and generalization, the paper proposes future research directions, including constructing network architectures with hard physical constraints, enhancing adaptability to complex grid scenarios, and developing self-evolving intelligent simulation frameworks to ensure future grid security.