Applications of fiber optic sensors to battery monitoring have been increasing due to the growing need of enhanced battery management systems with accurate state estimations. The goal of this review is to discuss the advancements enabling the practical implementation of battery internal parameter measurements including local temperature, strain, pressure, and refractive index for general operation, as well as the external measurements such as temperature gradients and vent gas sensing for thermal runaway imminent detection. A reasonable matching is discussed between fiber optic sensors of different range capabilities with battery systems of three levels of scales, namely electric vehicle and heavy-duty electric truck battery packs, and grid-scale battery systems. The advantages of fiber optic sensors over electrical sensors are discussed, while electrochemical stability issues of fiber-implanted batteries are critically assessed. This review also includes the estimated sensing system costs for typical fiber optic sensors and identifies the high interrogation cost as one of the limitations in their practical deployment into batteries. Finally, future perspectives are considered in the implementation of fiber optics into high-value battery applications such as grid-scale energy storage fault detection and prediction systems.