  Next-generation CMB satellite concepts (LiteBIRD, CORE, PIXIE, PICO) are
being proposed to detect the primordial CMB B-mode polarization at large
angular scales in the sky for tensor-to-scalar ratio values of ${r \lesssim
10^{-3}}$. Yet undetected, primordial CMB B-modes will provide the unique
signature of the primordial gravitational waves of quantum origin predicted by
inflation. We present recent forecasts on the detection of the primordial CMB
B-modes in the presence of astrophysical foregrounds and gravitational lensing
effects, in the context of the proposed CMB space mission CORE. We also discuss
the problem of foregrounds and component separation for the search for
primordial B-modes, and highlight specific challenges in this context:
frequency range, spectral degeneracies, foreground modelling, spectral
averaging effects.
