Lithium-ion batteries have many advantages such as the high specific energy, the high specific power, the long calendar life, being environmentally friendly, and can be used without the memory effect. Thus this type of battery is widely used as the core component in many applications such as electric vehicles, portable electronic devices, and distributed energy storage systems. However, lithium-ion batteries can easily develop into thermal runaways due to the stress and abuse from mechanical, electrical, and thermal perspectives, posing a major threat to the overall safety of many battery systems. On the premise of passing the manufacturer's safety inspections, a variety of methods for monitoring and detecting thermal runaway events are developed to enhance the safety and robustness of lithium-ion batteries in different application scenarios. This paper thus summarizes the existing literature on this topic and presents a comparative study on the sensitivity of various monitoring and detection methods. Potential future research directions are also discussed in detail to further enhance the safety and robustness of lithium-ion battery systems.