Boron, the only non-metallic element in the third main group, has special electron-deficient properties, which results in a complex bonding mechanism. It has both the normal two-center-two-electron bonds and the multi-center-two-electron bonds for keeping balance of the electron distribution of the system, which makes it have a wide variety of allotropes. In contrast to the bulk counterparts, low-dimensional boron nanostructures have unique structures and special properties, so they have attracted extensive interests in recent years. In this paper, we systematically introduce the theoretical and experimental progress on zero-dimensional boron clusters, one-dimensional boron nanotubes/nanowires and two-dimensional boron nanostructures. The structure, properties and potential applications of the boron nanostructures have been summarized and discussed. Although, there are still great challenges in the controllable preparation and stability of the nanostructures, they will be expected to have exceptionally inherent properties to make them play an important role in the future nano-devices and electrochemical catalysis.