The problems of heavy oil rheology, accompanied by physical phenomena of the formation and destruction of coagulation disordered structures and aggregates as a result of the hydrodynamic interaction of particles (asphaltenes, paraffins, resins, and solid-phase particles) contained in the oil, which significantly affect its properties and flow, are considered and analyzed. Rheological models of viscous-plastic heavy oils are considered and developed, consistent with a variety of experimental data. New rheological models for viscous-plastic heavy oils are proposed, which make it possible to generalize many existing models. It is noted that the variety of rheological models for heavy oils is determined by the conditions for the formation of disordered structures in the bulk of the oil flow. For heavy oils, a nonlinear equation for filtration in porous media is proposed, depending on the shear stress, pressure gradient, effective viscosity of the oil, and a number of other parameters. An analytical solution to this equation is proposed, which is consistent with the experimental data. Models for the settling rate and drag coefficient of particles in heavy oils are proposed. Applied problems of rheology aimed at improving the rheological properties of heavy oil during their processing as a result of creating a recirculation scheme at an operating oil refining unit are considered.