The rheology of glass melts is not restricted to Newtonian viscous flow, but it involves also non-Newtonian flow and viscoelasticity. The former one predominates in the steady-state flow at low deformation rates, the latter ones prevail during the initial state of stress generation and during the final state of flow and fracture under extreme deformation conditions. The whole range of rheological phenomena is demonstrated in this review article. Typical available experimental results and mathematical formulations are briefly given for single-phase glass melts. In this context the development of new equations gives rise to the introduction of a series of new definitions and conceptions which physically and mathematically characterize the different rheological behaviour of glass melts under various stress-strain conditions.