  We show that the spacetimes of domain wall solutions to the coupled
Einstein-scalar field equations with a given scalar field potential fall into
two classes, depending on whether or not reflection symmetry on the wall is
imposed. Solutions with reflection symmetry are dynamic, while the asymmetric
ones are static. Asymmetric walls are asymptotically flat on one side and
reduce to the Taub spacetime on the other. Examples of asymmetric thick walls
in D-dimensional spacetimes are given, and results on the thin-wall limit of
the dynamic, symmetric walls are extended to the asymmetric case. The
particular case of symmetric, static spacetimes is considered and a new family
of solutions, including previously known BPS walls, is presented.
