We present the results of theoretical and experimental studies of the heterojunction bipolar transistor. Our calculations are based on a new thermionic field-diffusion model which takes into account the dependence of the emitter efficiency on the height of the interface conduction band spike and tunneling across the spike. Based on this theory we derive analytical expressions for the current-voltage characteristics and relate the short-circuit common emitter current gain to the material parameters, doping levels, grading length, and device temperature. We demonstrate that the thermoemission transport across the interface spike limits the rate of increase in the collector current with the emitter-base voltage and, as a consequence, the maximum common emitter current gain. Tunneling also plays an important role, especially for abrupt heterojunctions. Our calculations reveal an important role played by grading of the composition of the emitter region in the vicinity of the heterointerface. Such grading decreases the barrier height at the interface and greatly enhances the emitter injection efficiency.