Media thermal conductivity is important in various heat-transfer processes. Many conventional fluid conductors suffered low conductivity and environmental issues. Therefore, research was active in finding out alternative systems, mostly relying on aqueous liquids that are low-cost and ecofriendly. After the emergence of carbon nanotubes (CNTs), with their many special structural, electrical and thermal properties, they have been examined for many applications, including heat-transfer processes. Adding CNTs to water yields CNT aqueous nanofluids that have been widely investigated as heat-transfer media. The literature shows that CNT addition improves water thermal conductivity and other water properties, such as viscosity, surface tension, freezing point and boiling point. The literature also shows that nanofluid thermal conductivity improvement is affected by CNT type and concentration, in addition to other factors such as surfactant addition. All these subjects were widely described in literature, focusing on experimental, modelling and theoretical accounts. Despite the wide literature, there exist inconsistencies and discrepancies between reports that need to be justified. In addition to technical papers, many reviews were published on various aspects of the subject including experimental results and mathematical modeling. However, the very basic question here is as follows: Why does adding CNT to water affect its thermal conductivity? In spite of the wide published literature, this issue was not targeted in a simple qualitative approach. This review provides a clear understanding of how CNTs improve thermal conductivity of aqueous nanofluids. A qualitative model is presented to explain mechanisms behind improvement as presented in the literature. 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 nanofluid characteristics as desired by varying types and concentrations of CNT and surfactant, and other factors.