After introduction of various types of magnetic fields in crystal growth, their main pros and cons for crystallization processes are discussed. It is shown that their further developments towards industrial maturity are bound up with the cardinal demands-increase of the process output, improvement of the crystal quality, and reduction of costs. In a further section, the advantages of travelling magnetic fields are presented. The central chapter is devoted to the target of the current KRIST (MA) over tildeG project-the development of an internal heater-magnet module for coupled generation of temperature and a travelling magnetic field, suitable for incorporation into industrial Czochralski pullers and vertical gradient freeze equipments. Amplitude, frequency and phase shift of the three-phase current are all adjustable and are combined with a dc component to control the crystallization process effectively. Results of accompanying numeric modelling are presented. The current state of crystal growth experiments in travelling magnetic field and first encouraging results are given. (C) 2007 Elsevier B.V. All rights reserved.