In this article, we review recent progress on AlGaN/GaN and InAlN/GaN metal-insulator-semiconductor high-electron-mobility transistors (MIS-HEMTs) using Al-based oxides, nitride dielectrics, SiO2 and high-k dielectrics. Although GaN MIS-HEMTs have been suffering from the instability of threshold voltage (VTH), recent interface technologies using in-situ SiNx and surface oxidation of (Al)GaN achieved excellent DC and dynamic performances of GaN MIS-HEMTs with stable VTH. Furthermore, a new design of the gate dielectric such as a nanolaminate structure has been applied to GaN HEMTs. GaN-based MIS-HEMTs sometimes showed sudden current saturation at forward gate bias, and we discuss effects of electronic states at insulator-semiconductor interfaces on current linearity of GaN MIS-HEMTs. Finally, we present effective surface passivation schemes in conjunction with field-plate structures and emerging device structures utilizing multi nanochannels under the gate region.