The object of this article is to review the development of ultrahigh-density, nanoscale data storage, i.e., "nanostorage". As a fundamentally new type of storage system, the recording mechanisms of nanostorage may be completely different to those of the traditional devices. Currently, two types of 'molecules' are being studied for potential application in nanostorage. One is molecular electronic elements including molecular wires, rectifiers, switches, and transistors. The other approach employs nanostructured materials such as nanotubes, nanowires, and nanoparticles. The challenges for nanostorage are not only the materials, ultrahigh data-densities, fabrication-costs, device operating temperatures and large-scale integration, but also the development of the physical principles and models. There are already some breakthroughs obtained, but it is still unclear what kind of nanostorage systems can ultimately replace the current silicon based transistors. A promising candidate may be a molecular-nanostructure hybrid device with sub-5 nm dimensions.