Lattice QCD in strong magnetic fields

12 pages, 12 figures, talk given by M. N. Chernodub at the 10th Workshop on Non-Perturbative QCD, June 8-12, 2009, Paris, FranceVacuum 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 electric dipole moment of quarks along the direction of the 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