  Heusler materials, initially discovered by Fritz Heusler more than a century
ago, have grown into a family of more than 1000 compounds, synthesized from
combinations of more than 40 elements. These materials show a wide range of
properties, but new properties are constantly being found. Most recently, by
incorporating heavy elements that can give rise to strong spin-orbit coupling
(SOC), non-trivial topological phases of matter, such as topological insulators
(TIs), have been discovered in Heusler materials. Moreover, the interplay of
symmetry, SOC and magnetic structure allows for the realization of a wide
variety of topological phases through Berry curvature design. Weyl points and
nodal lines can be manipulated by various external perturbations, which results
in exotic properties such as the chiral anomaly, and large anomalous spin and
topological Hall effects. The combination of a non-collinear magnetic structure
and Berry curvature gives rise a non-zero anomalous Hall effect, which was
first observed in the antiferromagnets Mn3Sn and Mn3Ge. Besides this k-space
Berry curvature, Heusler compounds with non-collinear magnetic structures also
possess real-space topological states in the form of magnetic antiskyrmions,
which have not yet been observed in other materials. The possibility of
directly manipulating the Berry curvature shows the importance of understanding
both the electronic and magnetic structures of Heusler compounds. Together,
with the new topological viewpoint and the high tunability, novel physical
properties and phenomena await discovery in Heusler compounds.
