  The abundance of semiconductors in our smartphones, computers, fiber optic
junctions, cars, light sources, photovoltaic and thermoelectric cells results
from the possibilities of controlling their properties through doping,
lighting, and applying various fields. This paper, a part of the volume
celebrating 100 years of the Polish Physical Society, presents a biased
selection of worthwhile results obtained by researchers at the Institute of
Physics, Polish Academy of Sciences relevant, as seen today, to topological
matter and spintronics. Comprehensive studies, combining materials development,
experimental investigations, and theoretical description of narrow-gap and
dilute-magnetic semiconductors have been especially significant in this
context. This survey also emphasizes, in an autobiographical tone, a half of a
century of the author's intellectual emotions accompanying the rise of ideas
and quantitative theories, allowing identifying the physics behind ongoing and
future observations.
