40 years of research on low-frequency (LF) noise and random-telegraph noise (RTN) in metallic and semiconducting nanowires (NWs) demonstrate the importance of defects and impurities to each system. The fluctuating interference of electrons in the local environment of a mobile bulk defect or impurity can lead to LF noise, RTN, and device-to-device variations in metallic and semiconducting NWs. Scattering centers leading to mobility fluctuations in semiconducting NWs include random dopant atoms and bulk defect clusters. Effective energy distributions for the relevant defects and impurities can be obtained from noise versus temperature measurements in conjunction with the Dutta-Horn model of LF noise for both metallic and semiconducting NWs. In semiconducting NWs configured as metal-oxide-semiconductor field-effect transistors, fluctuations in carrier number due to charge exchange with border traps, such as oxygen vacancies and/or their complexes with hydrogen in adjacent or surrounding dielectrics, often dominate or add to bulk noise sources.