Over two decades after carbon nanotubes started to attract interest for their seemingly huge prospects, their electrical properties are far from being used to the maximum potential. Composite materials based on carbon nanotubes still have conductivities several orders of magnitude below those of the tubes themselves. This study aims at understanding the reason for these limitations and the possibilities to overcome them. Based on and validated by real single-walled carbon nanotube (SWCNT) networks, a simple model is developed, which can bridge the gap between macroscale and nanoscale down to individual tube-tube contacts. The model is used to calculate the electrical properties of the SWCNT networks, both as-prepared and impregnated with an epoxy-amine polymer. The experimental results show that the polymer has a small effect on the large-scale network resistance. From the model results it is concluded that the main contribution to the conductivity of the network results from direct contacts, and that in their presence tunneling contacts contribute insignificantly to the conductivity. Preparing highly conductive polymer composites is only possible if the number of direct, low-resistance contacts in the network is sufficiently large and therefore these direct contacts play the key role.