Numerous studies have shown that nanofluids have superb physical properties, among which thermal conductivity has been studied most extensively but remains controversial. In this review article, we first present important milestones in experimental studies that show new features of the thermal conductivity of nanofluids, together with those that show no such special features. After a brief review of the physical mechanisms proposed to explain the thermal conductivity of nanofluids we present a critical review of the classical and new models used to predict the thermal conductivity behavior of nanofluids. We discuss some controversial issues such as data inconsistencies, the sufficiency and suitability of classical and new mechanisms, and the discrepancies between experimental data and model predictions. At the end of our review, we give some directions for future research in nanofluids and to aid researchers in resolving the controversial issues we are still facing in developing nanofluids with superior thermal properties and performance for high heat flux cooling and high efficiency applications.