  We write down the general conditions for N=1 supersymmetric four-dimensional
domain walls, deriving them from a ten-dimensional point of view using
generalized complex geometry. In cases where the compactification allows for a
truncation to a finite number of fields, we make contact with a
four-dimensional effective description. In the context of the AdS/CFT
correspondence, the equations can be applied to renormalization-group flows of
three-dimensional field theories. We allow for the presence of explicit brane
sources and show how supersymmetry restricts their location in a natural way.
