In this paper we review the results of our effort to grow layers and low-dimensional structures containing Cd_{1-x}Μn_{x}Te diluted magnetic semiconductor with relatively high values of Mn molar fraction x. A high quality of the structures grown so far is demonstrated by making use of results of several selected experiments. In the case of the epilayers having bulk-like thickness with x ≥ 0.7 we discuss, in particular, the magnetic phase diagram as well as we report on collective spin excitation (magnons) observed in Raman scattering experiments. The discussion of the growth of different quantum wells, including rectangular, digital, parabolic and wedge quantum wells, is accompanied by a brief overview of their optical and magnetooptical properties. These results include first measurements concerning magnetic polarons in quantum wells embedded in Cd_{1-x}Mn_{x}Te barriers with 0.4 ≤ x ≤ 0.8. Finally, we report on the present status of the search for dimensional effects in the spin-glass phase performed with the use of our specially designed superlattice structures.
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