GaN-on-SiC microwave devices are limited in power density by the thermal conductivity of the SiC substrate; to increase the potential for GaN microwave devices to increase their power density beyond the typical 10W/mm for reliable device operation, it is important to explore new substrates, in particular diamond substrates as their thermal conductivity can be as high as 2000W/mm allowing at least 3x increase in power density. We review the current state-of-the-art of GaN-on-diamond materials and devices, in the context of material and device reliability, material microstructure and thermal device management.