  This thesis deals with new backgrounds and concepts in Double Field Theory
(DFT), a T-Duality invariant reformulation of supergravity (SUGRA). We begin by
reviewing the basic concepts and notions of DFT. Afterwards, we turn to Double
Field Theory on group manifolds (DFT$_{\mathrm{WZW}}$). In order to obtain its
action and gauge transformations, Closed String Field Theory (CSFT)
computations are performed on a worldsheet, governed by a Wess-Zumino-Witten
model on a group manifold. We consider generalized diffeomorphisms and their
gauge algebra, which closes under a modified strong constraint. To explore the
connection between this theory and DFT, we recast it in terms of doubled
generalized objects and extrapolate it to all orders in fields. This yields a
generalized metric formulation and a flux formulation. We study the underlying
symmetries and field equations for both formulations. A novel feature in
DFT$_{\mathrm{WZW}}$ is an additional $2D$-diffeomorphism invariance. An
additional extended strong constraint which breaks the $2D$-diffeomorphism
invariance can be imposed to reduce DFT$_{\mathrm{WZW}}$ to DFT. Furthermore,
we perform a generalized Scherk-Schwarz compactification to recover the bosonic
subsector of half-maximal, electrically gauged supergravities. In this context,
we show how to construct twists for each embedding tensor solution explicitly
by using Maurer-Cartan forms. Finally, we generalize the ideas and notions from
DFT$_\mathrm{WZW}$ to geometric Exceptional Field Theory (gEFT). This allows us
to present a systematic construction for generalized parallelizable spaces in
dim M = 4 SL(5) Exceptional Field Theory (EFT). These spaces permit a unified
treatment of consistent maximally supersymmetric truncations of ten- and
eleven-dimensional supergravity in Generalized Geometry (GG) and their
systematic construction has always been an open question.
