The present paper describes improvements in the fracture resistance of epoxy polymers due to the addition of either (a) one-dimensional (1-D) carbon nanofibres (CNFs), or (b) two-dimensional (2-D) graphene nanoplatelets (GNPs), or (c) hybrid combinations of these carbon nanofillers (i.e. using both CNFs and GNPs). The effects of the dimensional shape and concentration (i.e. 0.0, 0.5, 1.0, 1.5 and 2.0 wt%) of the nanoscale carbon fillers are considered. The addition of CNFs, GNPs or hybrid combinations of CNFs and GNPs increases greatly the quasi-static fracture energy, GIc, of the epoxy due to these nanofillers inducing multiple intrinsic (e.g. interfacial debonding and void growth) and extrinsic (e.g. pull-out and bridging) toughening mechanisms. A mechanistic model is presented to quantify the contributions from the different toughening mechanisms induced by the CNF and the GNP fillers which result in the improvements observed in the fracture energy. The resistance of the epoxy, modified with either the GNPs or the CNFs, to cyclic-fatigue loading is also increased by the presence of the carbon nanofillers.