GaN-based high-electron mobility transistors (HEMTs) have brought unprecedented performance in terms of power, frequency, and efficiency. Application of metal-insulator-semiconductor (MIS) gate structure has enabled further development of these devices by improving the gate leakage characteristics, gate controllability, and stability, and offered several approaches to achieve E-mode operation desired for switching devices. Yet, bias-temperature instabilities (BTI) in GaN MIS transistors represent one of the major concerns. This paper reviews BTI in D- and E-mode GaN MISHEMTs and fully recess-gate E-mode devices (MISFETs). Special attention is given to discussion of existing models describing the defects distribution in the GaN-based MIS gate structures as well as related trapping mechanisms responsible for threshold voltage instabilities. Selected technological approaches for improving the dielectric/III-N interfaces and techniques for BTI investigation in GaN MISHEMTs and MISFETs are also outlined.