One-dimensional (1D) zinc oxide (ZnO) nanostructures have been extensively and intensively studied for several decades not only for their extraordinary chemical and physical properties, but also for their current and future different electronic and optoelectronic device applications. This review provides a brief overview of the progress of different synthesis methods and applications of 1D-ZnO nanostructures. Morphology of ZnO nanostructures grown by various methods and progress in the optical properties are briefly described. Using low-temperature photoluminescence (LTPL) study, detailed informations about the defect states and impurity of such nanostructures are reported. Improvement of field emission properties by modifying the edge of 1D-ZnO nanostructures is briefly discussed. Applications such as different sensors, field effect transistor, light-emitting diodes (LEDs), and photodetector are briefly reviewed. ZnO has large exciton binding energy (60 meV) and wide band gap (3.37 eV), which could lead to lasing action based on exciton recombination. As semiconductor devices are being aggressively scaled down, ZnO 1D nanostructures based resistive switching (RS) memory (resistance random access memory) is very attractive for nonvolatile memory applications. Switching properties and mechanisms of Ga-doped and undoped ZnO nanorods/NWs are briefly discussed. The present paper reviews the recent activities of the growth and applications of various 1D-ZnO nanostructures for sensor, LED, photodetector, laser, and RS memory devices.