A review on selected areas of research on low-dimensional structures consisting of diluted magnetic (semimagnetic) semiconductors is attempted. In the introductory part, after short historical preliminaries, we describe some early ideas and speculations concerning properties of such structures and we confront them with real results obtained in the course of their experimental investigations. Several issues are addressed to but, in view of the richness of the field, the review is by no means not pretending to be an exhaustive one. We begin with early studies of metal-insulator-semiconductor structures and progress to structures grown by molecular beam epitaxy. We discuss, in particular, the idea of a spin superlattice, type-I-to-type-II transition, wave functions mapping, and detailed determination of the profiles of realistic quantum wells. We put special emphasis on digital growth and, specifically, parabolic and half-parabolic quantum wells, use of tunable g-factor in studies of trions, self-assembled quantum dots, spin injection and, finally, on hybrid structures of ferromagnets and diluted magnetic semiconductor structures. The focus of the present paper is on work clone in the Institute of Physics of the Polish Academy of Sciences, mostly in the Laboratory of Growth and Physics of Low-Dimensional Crystals.