Autonomous vehicles (AVs) rely heavily on sensors to perceive their surrounding environment and then make decisions and act on them. However, these sensors have weaknesses, and are prone to failure, resulting in decision errors by vehicle controllers that pose significant challenges to their safe operation. To mitigate sensor failures, it is necessary to understand how they occur and how they affect the vehicle's behavior so that fault-tolerant and fault-masking strategies can be applied. This survey covers 108 publications and presents an overview of the sensors used in AVs today, categorizes the sensor's failures that can occur, such as radar interferences, ambiguities detection, or camera image failures, and provides an overview of mitigation strategies such as sensor fusion, redundancy, and sensor calibration. It also provides insights into research areas critical to improving safety in the autonomous vehicle industry, so that new or more in-depth research may emerge.