The rapid development of automated vehicles (AVs) promises to revolutionize transportation by enhancing safety and efficiency. However, ensuring their reliability in diverse real-world conditions remains a significant challenge, particularly due to rare and unexpected situations known as edge cases. Although numerous approaches exist for detecting edge cases, there is a notable lack of a comprehensive survey that systematically reviews these techniques. This paper fills this gap by presenting a practical, hierarchical review and systematic classification of edge case detection and assessment methodologies. Our classification is structured on two levels: first, categorizing detection approaches according to AV modules, including perception-related and trajectory-related edge cases; and second, based on underlying methodologies and theories guiding these techniques. We extend this taxonomy by introducing a new class called "knowledge-driven" approaches, which is largely overlooked in the literature. Additionally, we review the techniques and metrics for the evaluation of edge case detection methods and identified edge cases. To our knowledge, this is the first survey to comprehensively cover edge case detection methods across all AV subsystems, discuss knowledge-driven edge cases, and explore evaluation techniques for detection methods. This structured and multi-faceted analysis aims to facilitate targeted research and modular testing of AVs. Moreover, by identifying the strengths and weaknesses of various approaches and discussing the challenges and future directions, this survey intends to assist AV developers, researchers, and policymakers in enhancing the safety and reliability of automated driving (AD) systems through effective edge case detection.