Tellurium (Te), an attractive p-type van der Waals semiconductor, has been considered a promising candidate in electrical applications due to its unique one-dimensional chiral atomic-helical-chain structure, tunable bandgap, and ultrahigh hole mobility. This review summarizes recent advances in the controlled synthesis of Te semiconductor nanostructures, including one-dimensional tellurium nanowires and two-dimensional tellurene in the form of nanosheets and thin films. We further highlight emerging electrical applications of Te in field-effect transistors, logic circuits, photodetectors, memristors, and artificial synapse devices. Finally, current challenges and future opportunities for the commercialization of Te-based electronic and optoelectronic devices, particularly for neuromorphic and in-sensor computing systems, are discussed.