Understanding accurate thermal runaway (TR) mechanisms, a multiphase, multiphysics and multiscale phenomenon governed by complex interrelations among thermophysical factors, is critical for preventing fire-induced accidents in lithium-ion batteries (LIBs). Although conventional safety strategies using battery management systems (BMS) provide operational control and intervention, they exhibit fundamental safety gaps from early detection, prediction, and proactive response to emerging hazards. This work critically reviews recent advancements and identifies knowledge gaps in existing TR models, with a particular focus on enhancing predictive capabilities. It provides an in-depth analysis of both conventional physics-based and emerging data-driven models for addressing cell-level TR, venting, and cell-to-cell propagation. It systematically compares venting modeling approaches, from simplified pressure-driven equations to coupled CFD simulations, identifying computational efficiency versus accuracy trade-offs. Furthermore, it highlights the need for hybrid model combining physics and data-driven approaches to enhance accuracy and lower computational cost. The paper emphasizes the key safety deficiencies of current BMSs. Based on the critical analysis of existing models and safety gaps, this review proposes a conceptual framework for the future Battery Safety Management System (BSMS). This framework highlights how emerging predictive models and early warning signals could be integrated to complement existing BMS, serving as a roadmap for the future safety architecture design.