Owing to the three different orbital hybridizations carbon can adopt, the existence of various carbon nanoallotropes differing also in dimensionality has been already affirmed with other structures predicted and expected to emerge in the future. Despite numerous unique features and applications of 2D graphene, 1D carbon nanotubes, or 0D fullerenes, nanodiamonds, and carbon quantum dots, which have been already heavily explored, any of the existing carbon allotropes do not offer competitive magnetic properties. For challenging applications, carbon nanoallotropes are functionalized with magnetic species, especially of iron oxide nature, due to their interesting magnetic properties (superparamagnetism and strong magnetic response under external magnetic fields), easy availability, biocompatibility, and low cost. In addition, combination of iron oxides (magnetite, maghemite, hematite) and carbon nanostructures brings enhanced electrochemical performance and (photo)catalytic capability due to synergetic and cooperative effects. This work aims at reviewing these advanced applications of iron-oxide-supported nanocarbon composites where iron oxides play a diverse role. Various architectures of carbon/iron oxide nanocomposites, their synthetic procedures, physicochemical properties, and applications are discussed in details. A special attention is devoted to hybrids of carbon nanotubes and rare forms (mesoporous carbon, nanofoam) with magnetic iron oxide carriers for advanced environmental technologies. The review also covers the huge application potential of graphene/iron oxide nanocomposites in the field of energy storage, biomedicine, and remediation of environment. Among various discussed medical applications, magnetic composites of zero-dimensional fullerenes and carbon dots are emphasized as promising candidates for complex theranostics and dual magneto-fluorescence imaging.