Composite materials based on epoxy matrix and single-walled carbon nanotubes (SWCNTs) are able to exhibit outstanding improvements in physical properties when using a tailored covalent functionalization with matrix-based moieties containing terminal amines or epoxide rings. The proper choice of grafted moiety and integration protocol makes it feasible to tune the composite physical properties. At 0.5 wt% SWCNT loading, these composites exhibit up to 65% improvement in storage modulus, 91% improvement in tensile strength, and 65% improvement in toughness. A 15 °C increase in the glass transition temperature relative to the parent matrix was also achieved. This suggests that a highly improved interfacial bonding between matrix and filler, coupled to improved dispersion, are achieved. The degradation temperatures show an upshift in the range of 40-60 °C, which indicates superior thermal performance. Electrical conductivity ranges from ~10(-13) to ~10(-3) S cm(-1), which also shows the possibility of tuning the insulating or conductive behaviour of the composites. The chemical affinity of the functionalization moieties with the matrix and the unchanged molecular structure at the SWCNT/matrix interface are responsible for such improvements.