During the global energy transition, electric vehicles and electrochemical energy storage systems are rapidly gaining popularity, leading to a strong demand for lithium battery technology with high energy density and long lifespan. This technological advancement, however, hinges critically on resolving safety challenges posed by intrinsically reactive components particularly flammable polymeric separators, organic electrolyte systems, and high-capacity electrodes, which collectively elevate risks of thermal runaway (TR) under operational conditions. The strategic integration of smart polymeric materials that enable early detection of TR precursors (e.g., gas evolution, thermal spikes, voltage anomalies) and autonomously interrupt TR propagation chains has emerged as a vital paradigm for next-generation battery safety engineering. This paper begins with the development characteristics of thermal runaway in lithium batteries and analyzes recent breakthroughs in polymer-centric component design, multi-parameter sensing polymers, and TR propagation barriers. The discussion extends to intelligent material systems for emerging battery chemistries (e.g., solid-state, lithium-metal) and extreme operational environments, proposing design frameworks that leverage polymer multifunctionality for hierarchical safety mechanisms. These insights establish foundational principles for developing polymer-integrated lithium batteries that harmonize high energy density with intrinsic safety, addressing critical needs in sustainable energy infrastructure.