Anomalies are one of the cornerstones of relativistic quantum field theory.
They constrain possible fermion spectra of gauge theories and explain otherwise
forbidden processes such as de decay of the neutral pion into two photons.
In the recent years however anomalies play an ever bigger role in a totally different
realm of physics: condensed matter. In particular anomalies induce exotic new
transport phenomena such as the chiral magnetic and the chiral vortical effects.
I will give a pedestrian review of chiral anomalies and anomaly induced transport
phenoma and discuss some of its applications in a new exciting class of materials:
the Weyl semimetals.