  In the first half of the paper, we study in details NS-branes, including the
NS5-brane, the Kaluza-Klein monopole and the exotic $5_2^2$- or Q-brane,
together with Bianchi identities for NSNS (non)-geometric fluxes.
Four-dimensional Bianchi identities are generalized to ten dimensions with
non-constant fluxes, and get corrected by a source term in presence of an
NS-brane. The latter allows them to reduce to the expected Poisson equation.
Without sources, our Bianchi identities are also recovered by squaring a
nilpotent $Spin(D,D) \times \mathbb{R}^+$ Dirac operator. Generalized Geometry
allows us in addition to express the equations of motion explicitly in terms of
fluxes. In the second half, we perform a general analysis of ten-dimensional
geometric backgrounds with non-geometric fluxes, in the context of
$\beta$-supergravity. We determine a well-defined class of such vacua, that are
non-geometric in standard supergravity: they involve $\beta$-transforms, a
manifest symmetry of $\beta$-supergravity with isometries. We show as well that
these vacua belong to a geometric T-duality orbit.
