High-electron-mobility transistors (HEMTs) based on Al x Ga 1-x N/GaN heterostructures have great potential for applications in power electronics and radio-frequency (RF) applications. Operating under large bias and electric fields, hot electrons are present in the channel where they can activate pre-existing benign defects that cause scattering or carrier trapping, resulting in device degradation, such as threshold-voltage shifts and transconductance degradation. Here we report a comprehensive investigation of the electron transport properties of wurtzite-phase GaN and AlN and of an Al 0.25 Ga 0.75 N/GaN HEMT by solving the Boltzmann transport equation with a synchronous ensemble Monte Carlo technique and employing first-principles electronic properties, including the full energy bands, phonon dispersions, and electron-phonon scattering rates. We find that, for electron collisions with the highest-energy optical phonon mode, nonpolar scattering by optical phonons contributes comparable to polar scattering. Polar scattering with acoustic phonons, i.e., piezoelectric scattering, is found to be as important as the polar scattering with optical phonons for low energy electrons at room temperature. We compare the calculated high-field transport characteristics of bulk GaN with previously reported results. We also calculate the nonpolar acoustic deformation potential, nonpolar optical deformation potential, and high-field transport characteristics of bulk AlN. We find that inclusion of piezoelectric scattering results in a low-field electron mobility of ~450 cm 2 /(V·s), which is very close to the experimental value. Simulation results are presented for an Al 0.25 Ga 0.75 N/GaN HEMT, including electric field, average carrier kinetic energy, and drift velocity in the channel. Finally, we present the carrier energy distribution function in the conducting channel, which is key to accurately determine hot-carrier-caused device degradation, and identify possible routes to an improved device design.