Nanoscale structures need to be arranged into well-defined configurations in order to build integrated systems. Here we use a chemical-vapour deposition method with gas-phase catalyst delivery to direct the assembly of carbon nanotubes in a variety of predetermined orientations onto silicon/silica substrates, building them into one-, two- and three-dimensional arrangements. The preference of nanotubes to grow selectively on and normal to silica surfaces forces them to inherit the lithographically machined template topography of their substrates, allowing the sites of nucleation and the direction of growth to be controlled.