Lithium-ion batteries (LiBs) are seen as a viable option to meet the rising demand for energy storage. To meet this requirement, substantial research is being accomplished in battery materials as well as operational safety. LiBs are delicate and may fail if not handled properly. The failure modes and mechanisms for any system can be derived using different methodologies like failure mode effects analysis (FMEA) and failure mode methods effects analysis (FMMEA). FMMEA is used in this paper as it helps to identify the reliability of a system at the component level focusing on the physics causing the observed failures and should thus be superior to the more data-driven FMEA approach. Mitigation strategies in LiBs to overcome the failure modes can be categorized as intrinsic safety, additional protection devices, and fire inhibition and ventilation. Intrinsic safety involves modifications of materials in anode, cathode, and electrolyte. Additives added to the electrolyte enhance the properties assisting in the improvement of solid-electrolyte interphase and stability. Protection devices include vents, circuit breakers, fuses, current interrupt devices, and positive temperature coefficient devices. Battery thermal management is also a protection method to maintain the temperature below the threshold level, it includes air, liquid, and phase change material-based cooling. Fire identification at the preliminary stage and introducing fire suppressive additives is very critical. This review paper provides a brief overview of advancements in battery chemistries, relevant modes, methods, and mechanisms of potential failures, and finally the required mitigation strategies to overcome these failures.