This paper for the first time presents a comprehensive computational modeling approach for AlGaN/GaN high electron mobility transistors. Impact of the polarization charge at different material interfaces on the energy band profile as well as parasitic charge across the epitaxial stack is modeled and studied. Furthermore, impact of surface and bulk traps on two-dimensional electron gas, device characteristics, and gate leakage is accounted in this paper. For the first time, surface states modeled as donor type traps were correlated with gate leakage. Moreover, a new approach to accurately model the forward gate leakage in Schottky gate devices is proposed. Finally, impact of lattice and carrier heating is studied, while highlighting the relevance of carrier heating, lattice heating, and bulk traps over the device characteristics. In addition to this, modeling strategy for other critical aspects like parasitic charges, quantum effects, S/D Schottky contacts, and high field effects is presented. © 2016 IEEE.