[en] String theories on a background manifold with torsion are discussed. Candidate vacuum configurations are discussed for ten-dimensional superstrings. These are compactified on M₄ x K, where M₄ is four-dimensional and K is some compact six-dimensional manifold. Solutions with non-zero torsion on K are emphasized. The compactification problem is approached both from the effective field theory point of view and directly using string considerations. The construction of string theories in curved space with torsion is then discussed. Particular emphasis is put on the constraints on space-time supersymmetry in the Green-Schwarz approach. Two-dimensional non-linear sigma models are used to describe the propagation of strings in background geometries with torsion