  The long fascination antiferromagnetic materials have exerted on the
scientific community over about a century has been entirely renewed recently
with the discovery of several unexpected phenomena including various classes of
anomalous spin and charge Hall effects and unconventional magnonic transport,
but also homochiral magnetic entities such as skyrmions. With these
breakthroughs, antiferromagnets standout as a rich playground for the
investigation of novel topological behaviors, and as promising candidate
materials for disruptive low-power microelectronic applications. Remarkably,
the newly discovered phenomena are all related to the topology of the magnetic,
electronic or magnonic ground state of the antiferromagnets. This review
exposes how non-trivial topology emerges at different levels in
antiferromagnets and explores the novel mechanisms that have been discovered
recently. We also discuss how novel classes of quantum magnets could enrich the
currently expanding field of antiferromagnetic spintronics and how spin
transport can in turn favor a better understanding of exotic quantum
excitations.
