This paper reviews recent progress in the field of GaN/SiC heterojunction bipolar transistors. Key issues are identified and discussed. These include the comparison of a double-mesa and a selectively grown emitter structure, the evaluation of the GaN/SiC heterojunction and the problems faced when operating the devices in a common-emitter mode. A circuit simulation is presented indicating that common-emitter operation can be obtained for devices with low leakage current and modest gain.