Nanofluids—fluid suspensions of nanometer-sized particles—are a very important area of emerging technology and are playing an increasingly important role in the continuing advances of nanotechnology and biotechnology worldwide. They have enormously exciting potential applications and may revolutionize the field of heat transfer. This review is on the advances in our understanding of heat-conduction process in nanofluids. The emphasis centers on the thermal conductivity of nanofluids: its experimental data, proposed mechanisms responsible for its enhancement, and its predicting models. A relatively intensified effort has been made on determining thermal conductivity of nanofluids from experiments. While the detailed microstructure-conductivity relationship is still unknown, the data from these experiments have enabled some trends to be identified. Suggested microscopic reasons for the experimental finding of significant conductivity enhancement include the nanoparticle Brownian motion, the Brownian-motion-induced convection, the liquid layering at the liquid-particle interface, and the nanoparticle cluster/aggregate. Although there is a lack of agreement regarding the role of the first three effects, the last effect is generally accepted to be responsible for the reported conductivity enhancement. The available models of predicting conductivity of nanofluids all involve some empirical parameters that negate their predicting ability and application. The recently developed first-principles theory of thermal waves offers not only a macroscopic reason for experimental observations but also a model governing the microstructure-conductivity relationship without involving any empirical parameter.