Energy harvesting is a green technology that authorizes small electronic devices to be supplied for perpetual operation. It enables wireless sensors to be integrated in applications that previously were not feasible with conventional battery-powered designs. Intermittent computing and scheduling are the two central aspects of designing a Real-Time Energy Harvesting (RTEH) sensor, generally used to monitor a mission critical process. Traditional scheduling algorithms fail to timely execute the hard deadline tasks because they accommodate no fluctuations in power supply and therefore no intermittent computing. A suitable energy-harvesting-aware scheduling algorithm has been proposed so as to achieve a higher schedulability rate. Unlike the classical EDF (Earliest Deadline First) scheduler, the ED-H algorithm is idling and clairvoyant, with an improved performance in terms of the deadline missing ratio. This paper reviews the main advances in dynamic priority scheduling based on EDF for energy-neutral systems.