Nanocomposites of aligned multi-walled carbon nanotubes (CNTs) embedded in a polymer matrix yield a unique combination of thermal and electrical properties and mechanical strength. These properties are intimately related to the composite nanostructure and to the growth and processing conditions. The alignment of the tubes, the filling fraction and the contact junction between the nanotubes are key parameters controlling the composite electrical conductivity. For this purpose, a full description of the composite nanostructure is required. Among the non-destructive scanning probe techniques, scanning spreading resistance microscopy is found to be a powerful technique in identifying the carbon nanotubes with true nanometer resolution, thus competing with SEM and TEM imaging. Additionally, the technique provides valuable information about the electrical conduction mechanism within the composite structure. Indeed, by using a controlled contact force and an appropriate model of conduction at the nanoscale, the tip-CNT contact resistance, the CNT intrinsic resistance and the CNT-epoxy-CNT resistance junction are evaluated. This latter is found to be the factor controlling the overall electrical conductivity of the composite.