Embedded digital devices are progressively deployed in dependable or safety-critical systems. These devices undergo significant hardware ageing, particularly in harsh environments. This increases their likelihood of failure. It is crucial to understand ageing processes and to detect hardware degradation early for guaranteeing system dependability. In this survey, we review the core ageing mechanisms, and identify and categorize general working principles of ageing detection and monitoring techniques for Commercial-Off-The-Shelf (COTS) components that are prevalent in embedded systems: Field Programmable Gate Arrays (FPGAs), microcontrollers, Systems-on-Chips (SoCs), and their power supplies. From our review, we find that online techniques are more widely applied on FPGAs than on other components, and see a rising trend towards machine learning application for analysing hardware ageing. Based on the reviewed literature, we identify research opportunities and potential directions of interest in the field. With this work, we intend to facilitate future research by systematically presenting all main approaches in a concise way.