The formation processes of epoxy nanocomposites with carbon (nanotubes, graphene, and graphite), metal-containing, and aluminosilicate (montmorillonite and halloysite tubes) fillers are considered. A high reactivity of epoxy groups and a thermodynamic miscibility of epoxy oligomers with many substances make it possible to use diverse curing agents and to accomplish curing reactions under various technological conditions. Epoxy nanocomposites are designed to realize to the same extent the unique functional properties of nanoparticles: electric, magnetic, optical, chemical, and biological. The mutual effect of both a matrix and nanoparticles on the composite formation is discussed.