The quest to have an effective and efficient heat transfer fluids has been a subject of great research interest for several decades. Nanofluids are preeminent fluids that have garnered increased attention recently due to their enhanced thermal properties. Moreover, viscosity is an essential characteristic of nanofluids and for this reason, many research works have been conducted on this subject over the last few decades. In this work, attempt is made to present the viscosity model of nanofluids. In addition, efforts are put forth to examine the existing empirical, semiempirical, and analytical correlations utilized for the evaluation of viscosity of nanofluids. Furthermore, there are a number of factors influencing the viscosity of nanofluids which has necessitated this review work. These factors not only feature the nanoparticle concentration, sizes, and types, they also include the temperature of the nanofluid as well as the base fluid surfactant and stability. This review also discuss several industrial applications of nanofluids such as those used for electronic cooling, solar applications, heat exchangers, and automotive industry. The available experimental results show that the above mentioned parameters have considerable effect over viscosity of nanofluid. However, there is no general trend to describe the influence of particle sizes on increase in viscosity. The lowest enhancement in viscosity with increase in nanoparticle concentration in literature was graphite/engine oil nanofluid with improvement of 6.25% with volume concentration increasing from 1 to 5.5%. It has also been observed that many empirical models have been formulated on viscosity of nanofluid; however, there is no universally accepted model. This review leads to some directions for future research in nanofluids.