One-dimensional (1D) boron nanostructures are very potential for nanoscale electronic devices since their physical properties including electric transport and field emission have been found very promising as compared to other well-developed 1D nanomaterials. In this article, we review the current progress that has been made on 1D boron nanostructures in terms of theoretical prediction, synthetic techniques, characterizations and potential applications. To date, the synthesis of 1D boron nanostructures has been well-developed. The popular structures include nanowires, nanobelts, and nanocones. Some of these 1D nanostructures exhibited improved electric transport properties over bulk boron materials as well as promising field emission properties. By current experimental findings, 1D boron nanostructures are promising to be one of core materials for future nanodevices. More efforts are expected to be made in future on the controlled growth of 1D boron nanostructures and tailoring their physical properties.