  Magnetic topological materials represent a class of compounds whose
properties are strongly influenced by the topology of the electronic
wavefunctions coupled with the magnetic spin configuration. Such materials can
support chiral electronic channels of perfect conduction, and can be used for
an array of applications from information storage and control to
dissipationless spin and charge transport. Here, we review the theoretical and
experimental progress achieved in the field of magnetic topological materials
beginning with the theoretical prediction of the Quantum Anomalous Hall Effect
without Landau levels, and leading to the recent discoveries of magnetic Weyl
semimetals and antiferromagnetic topological insulators. We outline the recent
theoretical progress that resulted in the tabulation, for the first time, of
all magnetic symmetry group representations and topology. We describe several
experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and
an array of axionic and higher-order topological phases of matter as well as
survey future perspectives.
