Low-frequency electronic noise, also referred to as excess noise, is present in almost all electronic materials and devices. It is usually desirable to reduce this noise type since it directly contributes to the phase noise of electronic devices and communications systems. However, measurements of the low-frequency noise can also provide valuable information on the material quality and electron transport. In this dissertation research, we developed approaches for electronic noise spectroscopy and applied them to a range of electronic materials and devices, including GaN and diamond high-current diodes, antiferromagnetic semiconductors, and Weyl semimetal nanowires. The excess noise includes the 1/f and generation-recombination (G-R) noise with a Lorentzian type spectrum (f is the frequency). The 1/f noise can be an early indicator of electromigration damage and provide insight into the nature of reliability-limiting defects in materials and devices. The noise in most of the tested GaN devices had a characteristic 1/f spectrum at high and moderate currents, while some devices revealed G-R bulges at low currents. Temperature, current, and frequency dependences of noise suggest that the noise mechanism in GaN diodes is of recombination origin. We argue that the noise measurements at low currents can be used to efficiently assess the quality of GaN diodes. The G-R bulges are characteristic of diamond diodes with lower turn-on voltages. The characteristic trap time constants, extracted from the noise data, show a uniquely strong dependence on current. The noise spectral density of FePS3 was of the 1/f-type over most of the examined temperature range but revealed well-defined Lorentzian bulges, and increased strongly near the Néel temperature TN=118 K. The noise attained its minimum at temperature T~200 K, which was attributed to an interplay of two opposite trends in noise scaling – one for semiconductors and another for materials with phase transitions. The obtained results are important for proposed applications of antiferromagnetic semiconductors in spintronic devices.