Mathematical models are nowadays widely accepted as an indispensable tool in the design and operation of glass melting furnaces and feeders. Based on the design of a furnace, the process conditions and all material properties, these models determine not only the flows and temperature distribution in the melting tank and combustion chamber, but also other important data such as redox state, colourants concentrations, residence time distribution and indicators for furnace performance such as the fining, refining, mixing and homogenisation index. At TNO glass group, continuous improvements and extensive use by major glass producers of the TNO glass tank model, have lead to a detailed, rigorous and validated model. This paper discusses some typical examples of the use of mathematical models.