To describe the viscosity of oil, the author proposed a theory based on a new physical model, which takes into account the interaction of individual colloidal particles and their aggregates of fractal structure. This process is accompanied by the addition of individual particles to aggregates and by their separation under the action of shear stress, which is reflected in the energy consumption of the fluid movement and manifests itself as a dependence of the viscosity on the shear rate. The purpose of the review is to demonstrate the application of fractal viscosity theory to interpret the results of known experimental studies. The review also contains the results of new experimental studies of a model sample of oil to illustrate a number of statements of the theory. The detailed parameters of the physical model are specified, on the basis of which a fractal theory of viscosity is proposed; a system of two equations is obtained that allows to describe the dependence of viscosity on the shear rate and time. It is demonstrated that the conclusions drawn from the theory correspond to the known and newly obtained experimental data. The regularities of viscosity relaxation predicted experimentally by the theory with increasing and decreasing shear rates are confirmed. A methodology based on the laws of thermodynamics is proposed that allows to select the mode of shear rate action on heavy oil to reduce its viscosity.