Selected transport processes associated with continuously moving material undergoing thermal processing are reviewed. The different approaches of solving thermal materials processing problems are discussed. Several fundamental heat transfer problems related to thermal processing are identified and state-of-knowledge of the underlying physical processes are reviewed. Examples of single phase and phase-change convection heat transfer problems considered include convective transport from a flat moving surface, conjugate heat transfer in a moving material, combined convective and radiative heat transfer to a surface moving in an enclosure, film boiling over a moving isothermal surface and flow and heat transfer processes during coating of a flat moving surface. Materials processing applications where these generic transport problems arise are discussed, and problems needing both experimental and theoretical research attention are identified and discussed.