List of symbols 42 628 P. GORNERT (iii) The flux reaction technique. (iv) The solvent evaporation technique.The importance of these methods decreases from (i) to (iv). All methods have the advantage that growth of the crystallizing compound occurs a t temperatures from about 600 to 1300 "C which are lower than the corresponding melting temperatures.HTS growth therefore is the connecting link between hydrothermal and melt growth. The method is preferably used for the preparation of incongruently melting materials, materials which undergo a phase transition, high refractory ones and materials with very volatile constituents.An important disadvantage is the incorporation of solvent ions in the crystal. The largest progress regarding crystal size and quality has been reached by a carefully controlled growth technology of garnets especially Y,Pe,O,, (YIG) in PbO-PbF,-B,O, solvents as developed by TOLKSDORF (reviews : TOLKSDORF 1977 a) from Philips Hamburg. This material is industrially produced for applications in the microwave technique as tunable filters, oscillators, circulators, isolators, delay lines and power limiters.Problems of HTS growth are comprehensively treated in books published in 1975 by ELWELL and SCHEEL and in 1978 by TIMOFEEVA or in book articles by WANK- LYN and ELWELL (1974), BRICE (1973BRICE ( , 1977, GIESS and GHEZ (1975). The aim of this paper is to review some recent (including 1978) results regarding physicochemical processes in HTS, which have not been discussed in a collected form up to now. A large part of these investigations bases on the application of induced st,riations in garnet single crystals, which were grown by the slow cooling method. Although the topic of the paper deals above all with single crystal growth, results achieved by liquid phase epitaxy (LPE) are needed to understand the growth mechanism more in detail.