A comprehensive review of research and development on rheological characteristics of nanofluids for their advanced heat transfer applications is performed and reported in this paper. It identifies the research anomaly and importance on this topic besides analysing rheology of nanofluids. Various classical and recently developed viscosity models for nanofluids are presented and discussed. Nanofluids are classified as metallic and nonmetallic types and research findings on this key property of available nanofluids are analyzed. Effects of several important factors such as concentration of nanoparticles and temperature on viscosity of each type of nanofluids have been explicitly reviewed. Results from various research groups and predictions from viscosity models are also compared and discussed in detail. Role and importance of the viscosity in connection with other thermal properties and parameters for their thermal management applications are highlighted. Furthermore, the research challenges and needs in this important area of nanofluids are also revealed.