Wide-bandgap gallium nitride (GaN)-based semiconductors offer significant advantages over traditional Si-based semiconductors in terms of high-power and high-frequency operations. As it has superior properties, such as high operating temperatures, high-frequency operation, high breakdown electric field, and enhanced radiation resistance, GaN is applied in various fields, such as power electronic devices, renewable energy systems, light-emitting diodes, and radio frequency (RF) electronic devices. For example, GaN-based high-electron-mobility transistors (HEMTs) are used widely in various applications, such as 5G cellular networks, satellite communication, and radar systems. When a current flows through the transistor channels during operation, the self-heating effect (SHE) deriving from joule heat generation causes a significant increase in the temperature. Increases in the channel temperature reduce the carrier mobility and cause a shift in the threshold voltage, resulting in significant performance degradation. Moreover, temperature increases cause substantial lifetime reductions. Accordingly, GaN-based HEMTs are operated at a low power, although they have demonstrated high RF output power potential. The SHE is expected to be even more important in future advanced technology designs, such as gate-all-around field-effect transistor (GAAFET) and three-dimensional (3D) IC architectures. Materials with high thermal conductivities, such as silicon carbide (SiC) and diamond, are good candidates as substrates for heat dissipation in GaN-based semiconductors. However, the thermal boundary resistance (TBR) of the GaN/substrate interface is a bottleneck for heat dissipation. This bottleneck should be reduced optimally to enable full employment of the high thermal conductivity of the substrates. Here, we comprehensively review the experimental and simulation studies that report TBRs in GaN-on-SiC and GaN-on-diamond devices. The effects of the growth methods, growth conditions, integration methods, and interlayer structures on the TBR are summarized. This study provides guidelines for decreasing the TBR for thermal management in the design and implementation of GaN-based semiconductor devices.