Electrons in topological insulators possess unique electronic band structures and spin properties, promising a novel route to engineer material properties for electronics and energy science. Enhancing the surface state signal in electron transport is critical for both fundamental study of the surface states and future applications. Nanostructures of topological insulators naturally have large surface-to-volume ratios, effectively increasing the surface transport compared to the bulk contribution. Moreover, the unique morphology of topological insulator nanostructures results in various quantum effects of electronic states, which can tailor the surface band via quantum confinement. Here we review recent progress in topological insulator nanostructures. Material design and electron transport of topological insulator nanostructures are introduced, with an emphasis on the unique properties of nanostructures. A few examples of applications and future perspective in using these nanostructures are also discussed.