In this paper we review results of studies of two types of spatially g
raded quantum well structures containing various layers of diluted mag
netic semiconductors Cd1-xMnxTe or Cd1-x-yMnxMgyTe. The design of the
structures has been recently proposed by us and suitable samples have
been grown by a modified molecular beam epitaxy method. In the structu
res of the first type a digital profiling of the composition of the co
nstituent material in the growth direction allowed to produce quantum
wells with a specifically required shape of the confining potential (i
ncluding parabolic, half-parabolic, triangular, and trapezoidal). Such
samples were used for (i) determination of the conduction and valence
band offsets in MnTe/CdTe and MgTe/CdTe systems, (ii) for the demonst
ration of an enhanced exciton binding in a parabolic confining potenti
al as well as for (iii) demonstration of the possibility of ''spin-spl
itting engineering'' in diluted magnetic semiconductors quantum struct
ures. In the second type of the structures, a precise in-plane profili
ng of either quantum well width or the barrier width or n-type doping
intensity was realized. These structures were subsequently used for st
udies of the evolution of optical spectra with an increase in the conc
entration of confined two-dimensional gas of conduction electrons. PAC
S numbers: 73.20.Dx, 78.55.Et.