  General Relativity provides us with an extremely powerful tool to extract at
the same time astrophysical and cosmological information from the Stochastic
Gravitational Wave Backgrounds (SGWBs): the cross-correlation with other
cosmological tracers, since their anisotropies share a common origin and the
same perturbed geodesics. In this letter we explore the cross-correlation of
the cosmological and astrophysical SGWBs with Cosmic Microwave Background (CMB)
anisotropies, showing that future GW detectors, such as LISA or BBO, have the
ability to measure such cross-correlation signals. We also present, as a new
tool in this context, constrained realization maps of the SGWBs extracted from
the high-resolution CMB {\it Planck} maps. This technique allows, in the
low-noise regime, to faithfully reconstruct the expected SGWB map by starting
from CMB measurements.
