High Electron Mobility Transistors (HEMT) made of aluminum gallium nitride/gallium nitride (AlGaN/GaN) have become a major focus for all electronic devices based on gallium nitride due to its excellent system characteristics. AlGaN/GaN HEMTs have severe issues that degrade their performance and the drain current collapse (CC) is one of them. During switching operations, the CC increases the on-resistance (Ron) leading to an increase in device loss and temperature. This review features the basics related to the current collapse in HEMT and its significance in performance degradation. This paper is concerned with the various advancements reported in recent years to suppress CC in GaN HEMT. Various techniques such as passivation, illumination, free-standing GaN substrate, GaN cap layer including high resistivity GaN cap layer, buffer design, and field plates (FP) have been introduced by various researchers to combat CC. This review analysis will help researchers to employ suitable techniques in their HEMT design for future development.