  Double Field Theory (DFT) is a proposal to incorporate T-duality, a
distinctive symmetry of string theory, as a symmetry of a field theory defined
on a double configuration space. The aim of this review is to provide a
pedagogical presentation of DFT and its applications. We first introduce some
basic ideas on T-duality and supergravity in order to proceed to the
construction of generalized diffeomorphisms and an invariant action on the
double space. Steps towards the construction of a geometry on the double space
are discussed. We then address generalized Scherk-Schwarz compactifications of
DFT and their connection to gauged supergravity and flux compactifications. We
also discuss U-duality extensions, and present a brief parcours on world-sheet
approaches to DFT. Finally, we provide a summary of other developments and
applications that are not discussed in detail in the review.
