AlGaN/GaN based high electron mobility transistors (HEMTs) are excellent candidates for high power and low-noise applications from RF through the millimeter wave. However, output power scaling in conventional device designs has proven challenging, especially at high frequencies. As a design alternative, graded-channel HEMTs have shown improved DC and RF performance due to the design flexibility that enables tailoring the transconductance (gm) and device capacitances, while maintaining high speed. Experimentally, graded-channel devices have also demonstrated improved output power scaling without the need for field plates, as well as higher speed and lower noise at low current densities, compared to conventional HEMTs. To understand these results, we report a detailed study of graded-channel HEMTs. We find that the use of a graded-channel structure enables engineering of not only the charge distribution (which controls the gm and capacitances) but also the lateral electric field profile. In contrast to abrupt AlGaN/GaN HEMTs which traditionally use field plates to minimize the surface electric fields in the gate-drain region, graded channel HEMTs can achieve significantly reduced electric fields through channel engineering. This makes them promising for high performance millimeter-wave applications.