This work investigates the challenges associated with designing silicon-germanium (SiGe) analog and mixed-signal circuits capable of operating reliably in extreme environment conditions. Three extreme environment operational conditions, namely, operation over an extremely wide temperature range, operation at extremely low temperatures, and operation under radiation exposure, are considered. As a representative for critical analog building blocks, bandgap voltage reference (BGR) circuit is chosen. Several architectures of the BGRs are implemented in two SiGe BiCMOS technology platforms. The effects of wide-temperature operation, deep cryogenic operation, and proton and x-ray irradiation on the performance of BGRs are investigated. The impact of Ge profile shape on BGR's wide-temperature performance is also addressed. Single-event transient response of the BGR circuit is studied through microbeam experiments. In addition, proton radiation response of high-voltage transistors, implemented in a low-voltage SiGe platform, is investigated. A platform consisting of a high-speed comparator, digital-to-analog (DAC) converter, and a high-speed flash analog-to-digital (ADC) converter is designed to facilitate the evaluation of the extreme environment capabilities of SiGe data converters. Room temperature measurement results are presented and predictions on how temperature and radiation will impact their key electrical properties are provided.