A review of the current knowledge on carbon fullerenes doped with foreign atoms and heteroatom-containing fullerene-like structures and nanotubes is provided. Strong covalent bonds lend high specificity and stabilize the hollow-cage and symmetric structure of these moieties. These structures are distinct from noble-gas and metallic clusters, where either weak van der Waals forces or stronger metallic bonds, which are not very specific, hold the cluster atoms together. In the latter kind of clusters, atoms gain stability through close packing and large coordination numbers and consequently they cannot afford a hollow core. Nonetheless some intermetallic nanoparticles exhibit truncated icosahedral symmetry. The field is divided, somewhat artificially, into two separate categories. One family consists of fullerene-like clusters assembled from different atoms which do not have a bulk counterpart of similar chemical formula. The other group is that of fullerene-like nanostructures which are obtained mainly from ubiquitous 2-D layered compounds; various elements and compounds with 3-D character and also from certain metallic alloys. It is shown that nanoparticles of 2-D compounds are unstable in the planar form and they reconstruct into hollow-cage nanoparticles, spontaneously. Nanosolids of this kind may reveal vastly different properties from their bulk predecessors. Numerous applications for the doped and heteroatom fullerene-like materials in the fields of catalysis, lubrication, electronic and photonic devices, alternative energy sources, etc. are expected upon further study and development.