  The recent demonstrations of electrical manipulation and detection of
antiferromagnetic spins have opened up a chapter in the spintronics story. In
this article, we review the emerging research field that is exploring synergies
between antiferromagnetic spintronics and topological structures in real and
momentum space. Active topics include proposals to realize Majorana fermions in
an antiferromagnetic topological superconductors, to control topological
protection of Dirac points by manipulating antiferromagnetic order parameters,
and to exploit the anomalous and topological Hall effects of zero net moment
antiferromagnets. We explain the basic physics concepts behind these proposals,
and discuss potential applications of topological antiferromagnetic
spintronics.
