Abstract The paper reviews recent publications in fluid mechanics which are relevant to the mathematical modelling of glass melting and glass fabrication processes. The development of computers using parallel processors has opened the way to the much more rapid solution of problems involving many mesh points. Considerable progress has been made in the solution of problems involving free surfaces, which may be either moving or stationary. Difficulties arise in problems which involve interfaces between solid, liquid and gaseous phases, since mathematical discontinuities may arise in these regions. Attention is drawn to studies of polymer processes which are often similar to those used in the glass industry.