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We review the status of domain walls in N=1 supergravity theories for the vacuum domain walls as well as dilatonic domain walls. We concentrate on a systematic analysis of the nature of the ...space-time in these domain wall backgrounds and the special role that supersymmetry is playing in determining the nature of such configurations. Isotropic vacuum domain walls that can exist between isolated minima of an N=1 supergravity matter potential fall into three classes: (i) extreme walls, which are static planar walls between supersymmetric minima, (ii) non-extreme walls, which are expanding bubbles with two centres and (iii) ultra-extreme walls, which are bubbles of false vacuum decay. Dilatonic walls arise in N=1 supergravity with a general coupling of the linear supermultiplet. The dilaton field, a scalar component of the linear multiplet, has no perturbative self-interaction, but couples to the matter potential responsible for the formation of the wall. The dilaton drastically changes the global space-time properties of the wall. For the extreme ones the spacetime structure depends on the strength of the dilaton coupling, while for non- and ultra-extreme solutions one always encounters naked singularities (in the absence of non-perturbative corrections to the dilaton potential). Non-perturbative effects may modify the dilaton coupling so that it has a discrete non-compact symmetry (S-duality). In this case the non-and ultra-extreme solutions can reduce to the singularity-free vacuum domain wall solutions. We also summarize domain wall configurations within the effective theory of N=1 superstring vacua, with and without inclusion of non-perturbative string effects, and also provide a comparison with other topological defects of perturbative string vacua.
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