  In this review we discuss the global geometry of noncommutative field
theories from a deformation point of view: The space-times under consideration
are deformations of classical space-time manifolds using star products. Then
matter fields are encoded in deformation quantizations of vector bundles over
the classical space-time. For gauge theories we establish a notion of
deformation quantization of a principal fiber bundle and show how the
deformation of associated vector bundles can be obtained.
