**Abstract: ** The generalized geometry and Courant algebroids provide a natural framework for the description of various aspects of the string theory. Einstein-Hilbert action for the gravity is defined using the scalar curvature of the Levi-Civita connection corresponding to the background metric. It is thus natural to consider the generalizations of this idea in the framework of the generalized geometry. Essential definitions of the generalized geometry, Courant algebroids and Courant algebroid connections are recalled. We show how the curvature tensor can be defined in order to give a well-behaved scalar curvature. One can use the these objects to re-derive and geometrically explain certain non-trivial equivalences appearing in the string theory.