I will give an overview of the requirements that a generic supersymmetric theory must fulfill in order to possibly admit a supersymmetry breaking vacuum that is at least metastable. A particularly strong and simple constraint universally emerges from the requirement that the scalar superpartners of the Goldstino fermions should not be tachyonic. This primarily concerns the curvature of the scalar manifold and provides a very useful discrimination tool. I will derive the main results for globally supersymmetric theories and then report on the generalization to supergravity theories, discussing sequentially all the allowednumbers of supersymmetries in four dimensions. I will then illustrate the implications of the derived constraints in the context of string models and the search for de Sitter vacua in these theories. I will finally comment on some open problems and other possible issues concerning supersymmetry breaking.

Ecole Polytechnique Fédérale de Lausanne