  We present a brief review of experimental and theoretical papers on studies
of electron transport and magnetic properties in manganese-based compounds
Mn$_2$YZ and Mn$_3$Z (Y = V, Cr, Fe, Co, Ni, etc.; Z = Al, Ge, Sn, Si, Pt,
etc.). It has been shown that in the electronic subsystem of Mn$_2$YZ
compounds, the states of a half-metallic ferromagnet and a spin gapless
semiconductor can arise with the realization of various magnetic states, such
as a ferromagnet, a compensated ferrimagnet, and a frustrated antiferromagnet.
Binary compounds Mn$_3$Z have the properties of a half-metallic ferromagnet and
a topological semimetal with a large anomalous Hall effect, spin Hall effect,
spin Nernst effect, and thermal Hall effect. Their magnetic states are also
very diverse: from a ferrimagnet and an antiferromagnet to a compensated
ferrimagnet and a frustrated antiferromagnet, as well as an antiferromagnet
with a kagome-type lattice. It has been demonstrated that the electronic and
magnetic properties of such materials are very sensitive to external influences
(temperature, magnetic field, external pressure), as well as the processing
method (cast, rapidly quenched, nanostructured, etc.). Knowledge of the
regularities in the behavior of the electronic and magnetic characteristics of
Mn$_2$YAl and Mn$_3$Z compounds can be used for applications in micro- and
nanoelectronics and spintronics.
