  The focus of this PhD thesis is on applications, new developments and
extensions of the noncommutative gravity theory proposed by Julius Wess and his
group.
  In part one we propose an extension of the usual symmetry reduction procedure
to noncommutative gravity. We classify in the case of abelian Drinfel'd twists
all consistent deformations of spatially flat Friedmann-Robertson-Walker
cosmologies and of the Schwarzschild black hole. The deformed symmetry
structure allows us to obtain exact solutions of the noncommutative Einstein
equations in many of our models.
  In part two we develop a new formalism for quantum field theory on
noncommutative curved spacetimes by combining methods from the algebraic
approach to quantum field theory with noncommutative differential geometry. We
also study explicit examples of deformed wave operators and find that there can
be noncommutative corrections even on the level of free field theories. The
convergent deformation of simple toy models is investigated and it is found
that these theories have an improved behaviour at short distances, i.e. in the
ultraviolet.
  In part three we study homomorphisms between and connections on
noncommutative vector bundles. We prove that all homomorphisms and connections
of the deformed theory can be obtained by applying a quantization isomorphism
to undeformed homomorphisms and connections. The extension of homomorphisms and
connections to tensor products of bimodules is clarified. As a nontrivial
application of the new mathematical formalism we extend our studies of exact
noncommutative gravity solutions to more general deformations.
