This chapter is devoted to the study the viscosity and rheology of nanofluids. Studying the properties of viscosity in nanofluids requires first analyzing it in a simple liquid. The chapter begins with discussion of this issue. The next Section discusses the theory of viscosity of coarse dispersed liquids. Special attention is paid to the analysis of the momentum transfer mechanism in such a system, which determines its viscosity. The experimental data on the study of the viscosity of nanofluids and data on its MD modeling are presented in Sect. 3.3. The next two Sections of this chapter are devoted to a discussion of the rheology of nanofluids with conventional spherical nanoparticles. The analysis of viscosity and rheology of nanofluids with CNTs is presented in Sect. 3.6. All necessary experimental data are presented here. The nanofluids with both SWCNTs and MWCNTs are considered. Since nanofluids with CNTs in a number of cases demonstrate viscoelastic properties, the necessary experimental data for studying their microrheology are presented in Sect. 3.7. The last section of the chapter discusses MD simulation of the rheology of nanofluids with CNTs.