We consider classical supersymmetric chiral models of field theory and focus our attention on the geometrical aspects of such theories. A characteristic feature of such models is that the interaction is not introduced by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the target manifold. In many aspects these models are analogous to gauge theories and, as became clear recently, they are also important for superstring theory, which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.