Many challenges remain in the effort to realize the exceptional properties of carbon nanotubes (CNT) in composite materials. Here, we report on electrically conductive composites fabricated via infiltration of CNT-based aerogels. The ultra low-density, high conductivity, and extraordinary robustness of the CNT aerogels make them ideal scaffolds around which to create conductive composites. Infiltrating the aerogels with various insulating materials (e.g. epoxy and silica) resulted in composites with electrical conductivities over 1 Scm-1 with as little as 1 vol% nanotube content. The electrical conductivity observed in the composites was remarkably close to that of the CNT scaffold in all cases.