Magnetic skyrmions are topologically stable spin configurations, which usually originate from chiral interactions known as Dzyaloshinskii-Moriya interactions. Skyrmion lattices were initially observed in bulk non-centrosymmetric crystals, but have more recently been noted in ultrathin films, where their existence is explained by interfacial Dzyaloshinskii-Moriya interactions induced by the proximity to an adjacent layer with strong spin-orbit coupling. Skyrmions are promising candidates as information carriers for future information-processing devices due to their small size (down to a few nanometres) and to the very small current densities needed to displace skyrmion lattices. However, any practical application will probably require the creation, manipulation and detection of isolated skyrmions in magnetic thin-film nanostructures. Here, we demonstrate by numerical investigations that an isolated skyrmion can be a stable configuration in a nanostructure, can be locally nucleated by injection of spin-polarized current, and can be displaced by current-induced spin torques, even in the presence of large defects.