The emergence of gallium nitride high-electron-mobility transistor (GaN HEMT) devices has the potential to deliver high power and high frequency with performances surpassing mainstream silicon and other advanced semiconductor field-effect transistor (FET) technologies. Nevertheless, HEMT devices suffer from certain parasitic and reliability concerns that limit their performance. This paper aims to review the latest experimental evidence regarding HEMT technologies on the parasitic issues that affect aluminum gallium nitride (AlGaN)/GaN HEMTs. The first part of this review provides a brief introduction to AlGaN/GaN HEMT technologies, and the second part outlines the challenges often faced during HEMT fabrication, such as normally-on operation, self-heating effects, current collapse, peak electric field distribution, gate leakages, and high ohmic contact resistance. Finally, a number of effective approaches to enhancing the device’s performance are addressed.