  We study ten-dimensional supersymmetric vacua with NSNS non-geometric fluxes,
in the framework of $\beta$-supergravity. We first provide expressions for the
fermionic supersymmetry variations. Specifying a compactification ansatz to
four dimensions, we deduce internal Killing spinor equations. These
supersymmetry conditions are then reformulated in terms of pure spinors,
similarly to standard supergravity vacua admitting an SU(3)xSU(3) structure in
Generalized Complex Geometry. The standard d-H acting on the pure spinors is
traded for a generalized Dirac operator D, depending here on the non-geometric
fluxes. Rewriting it with an exponential of the bivector $\beta$ leads us to
discuss the geometrical characterisation of the vacua in terms of a
$\beta$-twist, in analogy to the standard twist by the b-field. Thanks to D, we
also propose a general expression for the superpotential to be obtained from
standard supergravities or $\beta$-supergravity, and verify its agreement with
formulas of the literature. We finally comment on the Ramond-Ramond sector, and
discuss a possible relation to intermediate or dynamical SU(2) structure
solutions.
