Dirac structures were introduced by Winstein and Courant in 1990 in order to unify Poisson and pre-symplectic manifolds. Generalized complex structures were introduced by Hitchen and further investigation by Gualtieri, in order to unify symplectic and complex geometry. In this thesis we introduce calibrated complex structures on the generalized tangent bundle of a Riemannian manifold M and their relationship to the Riemannian geometry of M and we survey a concept of integrability of complex structures.