  Weyl semimetals are conductors whose low-energy bulk excitations are Weyl
fermions, whereas their surfaces possess metallic Fermi arc surface states.
These Fermi arc surface states are protected by a topological invariant
associated with the bulk electronic wavefunctions of the material. Recently, it
has been shown that the TaAs and NbAs classes of materials harbor such a state
of topological matter. We review the basic phenomena and experimental history
of the discovery of the first Weyl semimetals, starting with the observation of
topological Fermi arcs and Weyl nodes in TaAs and NbAs by angle and
spin-resolved surface and bulk sensitive photoemission spectroscopy and
continuing through magnetotransport measurements reporting the
Adler-Bell-Jackiw chiral anomaly. We hope that this article provides a useful
introduction to the theory of Weyl semimetals, a summary of recent experimental
discoveries, and a guideline to future directions.
