Quickest Detection, which refers to real-time detection of abrupt changes in the behavior of an observed signal or time series as quickly as possible after they occur, is essential to enable safety, security, and dependability of cyber-physical systems (CPS). Real-Time Machine Learning (RTML) has the potential to achieve quickest detection. However, Machine learning lacks the necessary mathematical framework to provide guarantees on correctness. The integration of machine learning with quickest detection not only creates new research opportunities with major societal implications, but also poses new research challenges in safety, security, and dependability.We will go through a comprehensive survey of the existing literature, identifying trends, challenges and presenting  novel findings in the area.