Realization of the full potentials of heterostructure bipolar devices with high gain and low noise performance requires qualitatively reliable and quantitatively precise predictive process and performance simulation models. In this review article, the details of the recently proposed extended drift-diffusion model is presented for determining the effect of band offsets on the static current and 1/f noise properties of heterojunction bipolar transistors (HBTs). The model satisfies boundary conditions that govern the carrier transport across the heterointerface and satisfy the current continuity by coupling the electron-hole recombination current across the space charge region to the minority diffusion current in the bulk regions. It is shown that the intrinsic junction resistance to the diffusing minority electrons across the heteroemitter depletion region is stronger (weaker) at small (high) forward biases as compared with that to the recombined electrons and holes. Increasing bias causes a change of nature of 1/f noise from recombination to diffusion type in HBTs. The model should be useful in understanding the effects of interface properties on current transport and 1/f noise performance of HBTs.