  A future detection of the Stochastic Gravitational Wave Background (SGWB)
with GW experiments is expected to open a new window on early universe
cosmology and on the astrophysics of compact objects. In this paper we study
SGWB anisotropies, that can offer new tools to discriminate between different
sources of GWs. In particular, the cosmological SGWB inherits its anisotropies
both (i) at its production and (ii) during its propagation through our
perturbed universe. Concerning (i), we show that it typically leads to
anisotropies with order one dependence on frequency. We then compute the effect
of (ii) through a Boltzmann approach, including contributions of both
large-scale scalar and tensor linearized perturbations. We also compute for the
first time the three-point function of the SGWB energy density, which can allow
one to extract information on GW non-Gaussianity with interferometers. Finally,
we include non-linear effects associated with long wavelength scalar
fluctuations, and compute the squeezed limit of the 3-point function for the
SGWB density contrast. Such limit satisfies a consistency relation,
conceptually similar to what found in the literature for the case of CMB
perturbations.
