Abstract Although amorphous carbons which may contain heteroatoms have been subjected to extensive study over many years, their structure and properties are not well understood. The discovery of the closed fullerene cages and related structures and their possible occurrence in amorphous carbons offers a new approach to the understanding of the chemical and physical properties of amorphous carbons. Most significantly electron micrographs of amorphous carbons and carbon blacks clearly depict the nonplanar nature of the carbon networks and three types of curved structures which may contain pentagonal rings are discussed. The nonplanarity of such networks may lead to voids in the structure which can trap free radicals (probably of the odd-alternate π-type) and this allows us to offer an explanation for the electrical conductivity and the magnetic properties of such materials. We also consider the effect of heteroatoms (N, S and O) in amorphous carbon structures.