The physical properties and especially viscosity and thermal conductivity are essential parameters for evaluating the heat transfer and flowing drag coefficients when designing a nanofluid system. This review presents a state of the art research progress of both the experimental and theoretical researches on viscosity and thermal conductivity of nanofluids. The results indicate that the viscosity and thermal conductivity of nanofluids are generally functions of particle loading, size, temperature and sometimes particle shape in their experimental range. Effect of material types is regularity on thermal conductivity but irregular on viscosity since the thermal conductivity of Graphene, CNTs, Au nanofluids is greatly higher than ordinary nanofluids but no orderliness could be found in viscosity for different particle types. Particle loading has a positive correlation with the relative viscosity and thermal conductivity but effects of particle size, shape, base fluid property and temperature are not unified. Although many influence factors have been considered, the main defect of the current modeling research is the failure of predicting the results in separate works due to the wide differences. Finally, the challenges and opportunities for the future studies are identified. (C) 2017 Elsevier B.V. All rights reserved.