Battery management systems (BMSs) are essential in ensuring the safe and stable operation of lithium-ion batteries (LIBs) in electric vehicles (EVs). Accurate sensor signals, particularly voltage, current, and temperature sensor signals, are essential for a BMS to perform functions such as state estimation, balance control, and fault diagnosis. The smooth operation of a BMS depends primarily on sensor signals, which provide current, voltage, and temperature information to maintain the battery pack in a safe running state. However, sensor failures and inaccurate measurement data can easily occur because of external interference and complex operating conditions. Therefore, an investigation into the fault diagnosis of battery sensors and fault-tolerant control (FTC) is necessary to ensure the normal operation of a BMS. This paper analyzes the modes of sensor faults, fault diagnosis methods, and fault-tolerant control techniques. First, the different modes of sensor faults are analyzed, and mathematical expressions for these faults are provided. Second, diagnostic methods for sensor faults based on models, signal processing, and data-driven methods are analyzed in detail. Finally, FTC techniques are introduced to ensure stable sensor operation. Based on an analysis of the research status of sensor fault diagnosis, a new development direction for sensor fault diagnosis is proposed.