Energy-storage technologies based on lithium-ion batteries are advancing rapidly. However, the occurrence of thermal runaway in batteries under extreme operating conditions poses serious safety concerns and potentially leads to severe accidents. To address the detection and early warning of battery thermal runaway faults, this study conducted a comprehensive review of recent advances in lithium battery fault monitoring and early warning in energy-storage systems from various physical perspectives. The focus was electrical, thermal, acoustic, and mechanical aspects, which provide effective insights for energy-storage system safety enhancement.