  Following the recent report of superconductivity in the bilayer nickelate
La$_{3}$Ni$_{2}$O$_{7}$ under pressure, we present an analysis of the
electronic and magnetic properties of La$_{3}$Ni$_{2}$O$_{7}$ as a function of
pressure using correlated density functional theory methods (DFT+$U$). At the
bare DFT level, the electronic structure of the ambient and high-pressure
phases of La$_{3}$Ni$_{2}$O$_{7}$are qualitatively similar. Upon including
local correlation effects within DFT+$U$ and allowing for magnetic ordering, we
find a delicate interplay between pressure and electronic correlations. Within
the pressure-correlations phase space, we identify a region (at $U$ values
consistent with constrained RPA) characterized by a high spin to low spin
transition with increasing pressure. In contrast to previous theoretical work
that only highlights the crucial role of the Ni-$d_{z^2}$ orbitals in this
material, we find that the Ni-$d_{x^{2}-y^{2}}$ orbitals are active upon
pressure and drive this rich magnetic landscape. This picture is preserved in
the presence of oxygen deficiencies.
