With the development of intelligent modern power systems, real-time sensing and monitoring of system operating conditions have become one of the enabling technologies. Due to their flexibility, robustness and broad serviceable scope, wireless sensor networks have become a promising candidate for achieving the condition monitoring in a power grid. In order to solve the problematic power supplies of the sensors, energy harvesting (EH) technology has attracted increasing research interest. The motivation of this paper is to investigate the profiles of harnessing the electric and magnetic fields and facilitate the further application of energy scavenging techniques in the context of power systems. In this paper, the fundamentals, current status, challenges, and future prospects of the two most applicable EH methods in the grid—magnetic field energy harvesting (MEH) and electric field energy harvesting (EEH) are reviewed. The characteristics of the magnetic field and electric field under typical scenarios in power systems is analyzed first. Then the MEH and EEH are classified and reviewed respectively according to the structural difference of energy harvesters, which have been further evaluated based on the comparison of advantages and disadvantages for the future development trend.