This chapter provides a comprehensive analysis of recent advancements and applications of High Electron Mobility Transistors (HEMTs), with a specific focus on AlGaN/GaN-based technologies. Various aspects of HEMT performance and optimization strategies are explored through a series of studies, ranging from DC characteristics and low-frequency noise to statistical modeling of manufacturing variability and temperature-dependent large-signal modeling. Additionally, comparisons between different HEMT configurations and materials are presented, highlighting their respective strengths and applications across different temperature regimes, including cryogenic temperatures and millimeter-wave frequencies. The synthesis of these findings underscores the continuous evolution and promising future of HEMTs in powering diverse electronic applications with enhanced performance, stability, and efficiency.