AbstractFrustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogues of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example, in which Weyl points can be manipulated in situ in the laboratory by applied fields. We discuss their appearance specifically in the breathing pyrochlore lattice, and give some general discussion of conditions to find Weyl magnons, and how they may be probed experimentally. Our work may inspire a re-examination of the magnetic excitations in many magnetically ordered systems.