New energy storage devices such as batteries and supercapacitors are widely used in various fields because of their irreplaceable excellent characteristics. Because there are relatively few monitoring parameters and limited understanding of their operation, they present problems in accurately predicting their state and controlling operation, such as state of charge, state of health, and early failure indicators. Poor monitoring can seriously affect the performance of energy storage devices. Therefore, to maximize the efficiency of new energy storage devices without damaging the equipment, it is important to make full use of sensing systems to accurately monitor important parameters such as voltage, current, temperature, and strain. These are highly related to their states. Hence, this paper reviews the sensing methods and divides them into two categories: embedded and non-embedded sensors. A variety of measurement methods used to measure the above parameters of various new energy storage devices such as batteries and supercapacitors are systematically summarized. The methods with different innovative points are listed, their advantages and disadvantages are summarized, and the application of optical fiber sensors is emphasized. Finally, the challenges and prospects for these studies are described. The intent is to encourage researchers in relevant fields to study the early warning of safety accidents from the root causes.