  Three-dimensional condensed matter incarnations of Weyl fermions generically
have a tilted dispersion---in sharp contrast with their elusive high-energy
relatives where a tilt is forbidden by Lorentz invariance, and with the
low-energy excitations of two-dimensional graphene sheets where a tilt is
forbidden by either crystalline or particle-hole symmetry. Very recently, a
number of materials (MoTe$_2$, LaAlGe and WTe$_2$) have been identified as
hosts of so-called type-II Weyl fermions whose dispersion is so strongly tilted
that a Fermi surface is formed, whereby the Weyl node becomes a singular point
connecting electron and hole pockets. We here predict that these systems have
remarkable properties in presence of magnetic fields. Most saliently, we show
that the nature of the chiral anomaly depends crucially on the relative angle
between the applied field and the tilt, and that an inversion-asymmetric
overtilting can give rise to a chiral charge reversal with violating the
conservation of chiral charges known from type-I Weyl materials. The
field-selective anomaly gives a novel magneto-optical resonance, providing an
experimental way to detect concealed Weyl nodes.
