The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer in bulk and when used as the matrix of carbon- and glass-fibre reinforced composites. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The fracture energy of the bulk epoxy polymer was increased from 77 to 212 J/m2 by the presence of 20 wt% of silica nanoparticles. The observed toughening mechanisms that were operative were (a) plastic shear-yield bands, and (b) debonding of the matrix from the silica nanoparticles, followed by plastic void-growth of the epoxy. The largest increases in toughness observed were for the 'hybrid' materials. Here a maximum fracture energy of 965 J/m2 was measured for a 'hybrid' epoxy polymer containing 9 wt% and 15 wt% of the rubber microparticles and silica nanoparticles, respectively. Most noteworthy was the observation that these increases in the toughness of the bulk polymers were found to be transferred to the fibre composites. Indeed, the interlaminar fracture energies for the fibre-composite materials were increased even further by a fibre-bridging toughening mechanism. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles, and for epoxy polymers containing micrometre-sized glass particles. The latter, relatively large, glass particles were investigated to establish whether a 'nano-effect', with respect to increasing the toughness of the epoxy bulk polymers, did indeed exist.