With the rise of Internet of Things (IoT), devices such as smartphones, embedded medical devices, smart home appliances as well as traditional computing platforms such as personal computers and servers have been increasingly targeted with a variety of cyber attacks. Due to limited hardware resources for embedded devices and difficulty in wide-coverage and on-time software updates, software-only cyber defense techniques, such as traditional anti-virus and malware detectors, do not offer a silver-bullet solution. Hardware-based security monitoring and protection techniques, therefore, have gained significant attention. Monitoring devices using side channel leakage information, e.g. power supply variation and electromagnetic (EM) radiation, is a promising avenue that promotes multiple directions in security and trust applications. In this paper, we provide a taxonomy of hardware-based monitoring techniques against different cyber and hardware attacks, highlight the potentials and unique challenges, and display how power-based side-channel instruction-level monitoring can offer suitable solutions to prevailing embedded device security issues. Further, we delineate approaches for future research directions.