Recent years have witnessed GaN-based devices delivering their promise of unprecedented power and frequency levels and demonstrating their capability as an able replacement for Si-based devices. High-electron-mobility transistors (HEMTs), a key representative architecture of GaN-based devices, are well-suited for high-power and high frequency device applications, owing to highly desirable III-nitride physical properties. However, these devices are still hounded by issues not previously encountered in their more established Si- and GaAs-based devices counterparts. Metal–insulator–semiconductor (MIS) structures are usually employed with varying degrees of success in sidestepping the major problematic issues such as excessive leakage current and current instability. While different insulator materials have been applied to GaN-based transistors, the properties of insulator/III-N interfaces are still not fully understood. This is mainly due to the difficulty of characterizing insulator/AlGaN interfaces in a MIS HEMT because of the two resulting interfaces: insulator/AlGaN and AlGaN/GaN, making the potential modulation rather complicated. Although there have been many reports of low interface-trap densities in HEMT MIS capacitors, several papers have incorrectly evaluated their capacitance–voltage (C–V) characteristics. A HEMT MIS structure typically shows a 2-step C–V behavior. However, several groups reported C–V curves without the characteristic step at the forward bias regime, which is likely to the high-density states at the insulator/AlGaN interface impeding the potential control of the AlGaN surface by the gate bias. In this review paper, first we describe critical issues and problems including leakage current, current collapse and threshold voltage instability in AlGaN/GaN HEMTs. Then we present interface properties, focusing on interface states, of GaN MIS systems using oxides, nitrides and high-κ dielectrics. Next, the properties of a variety of AlGaN/GaN MIS structures as well as different characterization methods, including our own photo-assisted C–V technique, essential for understanding and developing successful surface passivation and interface control schemes, are given in the subsequent section. Finally we highlight the important progress in GaN MIS interfaces that have recently pushed the frontier of nitride-based device technology.