  Vacuum of Quantum Chromodynamics in very strong (hadron-scale) magnetic
fields exhibits many interesting nonperturbative effects. Some of these effects
can be studied with the help of lattice simulations in quenched QCD. We review
our recent results demonstrating that very strong external magnetic fields lead
to (1) the enhancement of the chiral symmetry breaking [the quark condensate
rises with the increase of the external magnetic field]; (2) the chiral
magnetization of the QCD vacuum [spins of the quarks turn parallel to the
external field]; (3) the chiral magnetic effect [a CP-odd generation of the
electric current of quarks directed along the magnetic field]; (4) a CP-odd
generation of the anomalous quark electric dipole moment along the axis of
magnetic field. The first three effects were already predicted theoretically,
and subsequently observed numerically in our simulations, while the fourth
effect is a new result.
