Research on the thermophysical properties of nanofluids has been ongoing for almost thirty years due to their potential thermophysical applications in engineering. Already the first experiments to measure their thermal conductivity [43, 101, 173] have yielded excellent results. The addition of even small concentration of metal nanoparticles on the order of fractions of a percent enhanced the thermal conductivity of the base fluid by percents or even tens of percentages. The data from numerous measurements obtained over the years since then have been surprisingly contradictory. As it turned out, the thermal conductivity of nanofluids as well as their viscosity is not described by classical theories. The observed thermal conductivity coefficient of nanofluid compared to the corresponding values for the base fluid appeared to be quite large. Numerous mechanisms have been proposed to explain these large excesses. However, uncertainties still remain regarding these mechanisms. This is mainly because a consistent theory of thermal conductivity for simple fluids is still lacking. Nevertheless, the accumulated experimental material is so extensive and multidimensional that it allows, first, formulating general regularities of thermal conductivity of nanofluids, and, second, using the molecular dynamics method explaining at least qualitatively the observed effects. To ensure clarity and logical structure, this chapter starts with a discussion of the modern concept of thermal conductivity of fluids. The subsequent section describes thermal conductivity models for coarse dispersed fluids. The next section discusses the thermal conductivity of nanofluids with ordinary spherical particles. The following two sections discuss existing models of thermal conductivity of nanofluids and their simulation using the molecular dynamics method. The final section presents experimental data on the thermal conductivity of nanofluids containing CNTs.