The object of this thesis is to explore the low-frequency noise (LFN) in silicon-germanium (SiGe) heterojunction bipolar transistors (HBTs) and lateral bipolar junction transistors (BJTs). The LFN of SiGe HBTs and lateral BJTs not only determines the lowest detectable signal limit but also induces phase noise in high-frequency applications. Characterizing the LFN behavior and understanding the physical noise mechanism, therefore, are very important to improve the device and circuit performance. The dissertation achieves the object by investigating the LFN of SiGe HBTs and lateral BJTs with different structures for performance optimization and radiation tolerance, as well as by building models that explain the physical mechanism of LFN in these advance bipolar technologies. The scope of this research is separated into two main parts: the LFN of SiGe HBTs; and the LFN of lateral BJTs. The research in the LFN of SiGe HBTs includes investigating the effects of interfacial oxide (IFO), temperature, geometrical dimensions, and proton radiation. It also includes utilizing physical models to probe noise mechanisms. The research in the LFN of lateral BJTs includes exploring the effects of doping and geometrical dimensions. The research work is envisioned to enhance the understanding of LFN in SiGe HBTs and lateral BJTs.