  In this work a thorough study of a number of specific supersymmetric
sigma-models with extended supersymmetry is performed within the context of
generalised complex geometry. More specifically the supersymmetric
Wess-Zumino-Witten model on a variety of group manifolds was considered. By
explicitly calculating the admissible complex structures and the associated
pure spinors on the target manifold a full characterisation of the different
possible geometries is provided. By using this approach the various aspects of
generalised K\"ahler geometry can be studied in detail. Also considered are the
various isometries present in the model and duality relations linking the
different descriptions.
