  We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with four
supercharges, coupled to any number of vector and scalar multiplets in all
cases. We find that backgrounds with N=1 supersymmetry admit a null,
integrable, Killing vector field. There are two classes of N=2 backgrounds. The
spacetime in the first class admits a parallel null vector field and so it is a
pp-wave. The spacetime of the other class admits three Killing vector fields,
and a vector field that commutes with the three Killing directions. These
backgrounds are of cohomogeneity one with homogenous sections either
$\bR^{2,1}$ or $AdS_3$ and have an interpretation as domain walls. The N=3
backgrounds are locally maximally supersymmetric. There are N=3 backgrounds
which arise as discrete identifications of maximally supersymmetric ones. The
maximally supersymmetric backgrounds are locally isometric to either
$\bR^{3,1}$ or $AdS_4$.
