The thermal management challenge posed by gallium nitride (GaN) high-electron-mobility transistor (HEMT) technology has received much attention in the past decade. The peak amplification power density of these devices is limited by heat transfer at the device, substrate, package, and system levels. Thermal resistances within micrometers of the transistor junction can limit efficient heat spreading from active device regions into the substrate and can dominate the overall temperature rise. Gallium nitride composite substrates, which consist of AlGaN/GaN heterostructures with thickness of a few microns on a thicker non-GaN substrate, govern the thermal resistance associated with the "near-junction" region. Silicon and silicon carbide have been widely used as a substrate material, but the performance of GaN devices grown on these substrates is still severely limited by thermal constraints and associated reliability issues. The importance of effective junction-level heat conduction has motivated the development of composite substrates containing high-thermal-conductivity diamond, but these composites require careful attention to thermal resistances between the GaN and the diamond. This chapter reviews thermal conduction phenomena in GaN composite substrates containing Si, SiC, and diamond. The review discusses the governing conduction physics and overviews the relevant measurement techniques. The best available experimental data for GaN composite substrates as well as the relevant thermal modeling are presented. The review concludes with an assessment of the potential benefits of the use of diamond on the device thermal performance.