Machine Learning (ML) models, such as deep neural networks, are widely applied in autonomous systems to perform complex perception tasks. New dependability challenges arise when ML predictions are used in safety-critical applications, like autonomous cars and surgical robots. Thus, the use of fault tolerance mechanisms, such as safety monitors, is essential to ensure the safe behavior of the system despite the occurrence of faults. This paper presents an extensive literature review on safety monitoring of perception functions using ML in a safety-critical context. In this review, we structure the existing literature to highlight key factors to consider when designing such monitors: threat identification, requirements elicitation, detection of failure, reaction, and evaluation. We also highlight the ongoing challenges associated with safety monitoring and suggest directions for future research.