  We study the influence of strong external magnetic fields on gluonic and
fermionic observables in the QCD vacuum at zero and nonzero temperatures, via
lattice simulations with N_f=1+1+1 staggered quarks of physical masses. The
gluonic action density is found to undergo magnetic catalysis at low
temperatures and inverse magnetic catalysis near and above the transition
temperature, similar to the quark condensate. Moreover, the gluonic action
develops an anisotropy: the chromo-magnetic field parallel to the external
field is enhanced, while the chromo-electric field in this direction is
suppressed. We demonstrate that the same hierarchy is obtained using the
Euler-Heisenberg effective action. Conversely, the topological charge density
correlator does not reveal a significant anisotropy up to magnetic fields eB~1
GeV^2. Furthermore, we show that the pressure remains isotropic even for
nonzero magnetic fields, if it is defined through a compression of the system
at fixed external field. In contrast, if the flux of the field is kept fixed
during the compression -- which is the situation realized in the lattice
simulation -- the pressure develops an anisotropy. We estimate the quark and
gluonic contributions to this anisotropy, and relate them to the magnetization
of the QCD vacuum. After performing electric charge renormalization, we obtain
an estimate for the magnetization, which indicates that QCD is paramagnetic.
