Electron-rich allenes and heterocumulenes are commonly described by the regular notations of organic chemistry. Following on from published results and recent computational studies, we present here a host of crystallographic and reactivity data, as well as theoretical results, that indicate a highly non-canonical bonding situation in many members of this series. These must actually be interpreted as coordination compounds, in which carbon serves as a 'central atom' that interacts with its 'ligand sphere' via donor-acceptor bonds, even if these internal ligands themselves are carbon based. This captodative description is not limited to compounds that supposedly comprise a carbon(0) centre, a peculiar oxidation state that can be probed experimentally by geminal diauration. As the available data suggest that this unconventional interpretation of C-C and C-X bonds is more generally applicable than previously anticipated, it may well affect our understanding of organic chemistry in general.