Continuous liquid-to-glass transition is characterized by dramatic changes of the liquid structure, thermodynamics and dynamics in a comparatively narrow temperature range. The viscous flow modes of the matter are changing within this temperature range too. The interplay of the structural, thermodynamic, mechanical and dynamic parameters at the viscous flow is still a challenge. Near the glass transition temperature the cooperative diffusion and sliding determine the shear viscosity of the liquid and glass as well as the fragility and the strain rate sensitivity of the flow. In this chapter the theoretical aspects of the physics of viscous flow of glass-forming liquids and glasses are considered within the framework of the heterophase fluctuations model (HPFM), providing a mesoscopic description of the heterophase liquid states. Newtonian and non-Newtonian, Arrhenius and non-Arrhenius flow modes are considered as well as the crossover from the flow to inhomogeneous deformation of glass. The fragility, the strain rate sensitivity, and the fragile-to-strong liquid transformation are described.