Embedded digital devices, such as Field-Programmable Gate Arrays (FPGAs) and Systems on Chip (SoCs), are increasingly used in dependable or safety-critical systems. These commodity devices are subject to notable hardware ageing, which makes failures likely when used for an extended time. It is of vital importance to understand ageing processes and to detect hardware degradations early. In this survey, we describe the fundamental ageing mechanisms and review the main techniques for detecting ageing in FPGAs, microcontrollers, SoCs, and power supplies. The main goal of this work is to facilitate future research efforts in this field by presenting all main approaches in an organized way.