Automated vehicles promise to enhance transportation safety and efficiency. However, ensuring their reliability in real-world conditions remains challenging, particularly due to rare and unexpected situations known as edge cases. While numerous approaches exist for detecting edge cases, a comprehensive survey reviewing these techniques is lacking. This paper bridges this gap by presenting a hierarchical review and systematic classification of edge case detection and assessment methodologies. Our classification is structured on two levels: first, by AV modules, including perception and trajectory-related (encompassing prediction, planning, and control) sub-systems; and second, by underlying methodologies and theories guiding these techniques. Furthermore, we introduce "knowledge-driven" approaches, which complement data-driven methods by leveraging expert insights and domain knowledge to identify cases absent in training datasets. We then examine techniques and metrics for evaluating edge case detection methods, including detection performance (e.g., precision, recall, false positive rates), practical deployment (e.g., computational overhead, detection delay), and domain-specific measures (e.g., crash rates, severity analysis). We conclude by highlighting key challenges for edge case detection, including data availability and quality issues, validation and interpretability limitations, the sim2real gap, and computational constraints. The hierarchical classification and review of methods and assessment techniques in this survey enable modular and targeted testing frameworks by guiding the selection of detection methods for specific AV subsystems while considering methodological principles. It also supports practical testing by facilitating scenario generation in simulation and focused subsystem validation in the real world.