In power electronic circuits, enhancement mode (E-mode) devices play a vital role while realizing fail-safe operation.  Presence of in-built two-dimensional electron gas (2DEG), near the heterointerface in High Electron Mobility Transistors (HEMTs), make these devices very difficult and challenging for the researchers to achieve E-mode of operation. In this chapter, a comprehensive study has been performed first on AlGaAs/GaAs based HEMTs and gradually the study continued up to AlGaN/GaN based tri-gate fin-shaped HEMTs (FinHEMTs). In all these devices under consideration, efforts have been made to investigate the device operation with respect to 2DEG formation near the heterointerface and how it can be depleted in order to realize E-mode operation with reference to the existing literature. Moreover, as gate leakage current becoming an issue in smooth device characteristics, one section is dedicated towards explaining the different mechanisms governing this current scenario with respect to different operating temperatures in GaN-based HEMTs. It is very fascinating to accept that the recent advances in HEMT technology such as tri-gate FinHEMT structures are promising candidates not only for realizing E-mode operation but also supressing short channel effects while downscaling in accordance with Moore’s law.