  The last decade has witnessed great advancements in the science and
engineering of systems with unconventional band structures, seeded by studies
of graphene and topological insulators. While the band structure of graphene
simulates massless relativistic electrons in two dimensions, topological
insulators have bands that wind non-trivially over momentum space in a certain
abstract sense. Over the last couple of years, enthusiasm has been burgeoning
in another unconventional and topological (although, not quite in the same
sense as topological insulators) phase -- the Weyl Semimetal. In this phase,
electrons mimic Weyl fermions that are well-known in high-energy physics, and
inherit many of their properties, including an apparent violation of charge
conservation known as the Chiral Anomaly. In this review, we recap some of the
unusual transport properties of Weyl semimetals discussed in the literature so
far, focusing on signatures whose roots lie in the anomaly. We also mention
several proposed realizations of this phase in condensed matter systems, since
they were what arguably precipitated activity on Weyl semimetals in the first
place.
