This work investigates the effect of adding graphene nanoplatelets (GNP) and either a phase-separating carboxyl-terminated butadiene acrylonitrile rubber (CTBN) or a polysiloxane core–shell rubber (CSR) to an anhydride-cured epoxy polymer. The effect of adding a reactive diluent to the resin was also investigated. The relationship between the microstructure and the resultant electrical and mechanical properties was investigated. The fracture energy of the unmodified epoxy polymer increased from 125 to 668 J/m2 with the addition of 9 wt% CTBN and 12.5 % reactive diluent. The subsequent addition of GNP to the rubber systems decreased the fracture energy. The epoxy nanocomposites modified with only GNP exhibited only a modest increase in measured fracture energy. The major toughening mechanisms in the rubber-modified formulations were observed to be shear band yielding and cavitation of the rubber particles followed by plastic void growth of the epoxy matrix. The electrical conductivity of the hybrid systems was also investigated. It was observed that the conductivity of the nanocomposites improved when 0.5 wt% of GNP was added although this improvement was lost in a CTBN–GNP system while the conductivity was further improved in the CSR–GNP system over the GNP only system with low-CSR particle loadings. It is demonstrated that this behaviour can be directly attributed to the microstructure of the nanocomposite. The results demonstrate that separation of nanomodified phases at the microscale can be used to develop simultaneously tough and conductive composites.