Media thermal conductivity is important in various heat-transfer processes. Many conventional fluid conductors suffered low conductivity and environmental issues. Therefore, researchers developed efficient aqueous nanofluid conductors. Carbon nanotubes (CNTs) are widely studied to reach efficient, stable, low-cost and environmentally-friendly aqueous-nanofluids. This review provides a clear understanding of how CNTs improve thermal conductivity of aqueous nanofluids. A qualitative model is presented to explain literature mechanisms behind improvement. CNT type effects are discussed with other factors such as aspect ratio, Reynold number, dispersion quality, composition, temperature and additives. CNT functionalization is described. Relations to estimate nanofluid thermal conductivity are discussed. The model will help specialists to tailor CNT aqueous nanofluids as desired.