  We introduce the group field theory (GFT) formalism for non-perturbative
quantum gravity, and present it as a potential unifying framework for several
other quantum gravity approaches, i.e. loop quantum gravity and simplicial
quantum gravity ones. We then argue in favor of and present in detail what we
believe is a new GFT perspective on the emergence of continuum spacetime from
discrete quantum structures, based on the idea of quantum space as a condensed
matter system. We put forward a more specific, albeit still very much
tentative, proposal for the relevant phase of the GFT corresponding to the
continuum: a Bose-Einstein condensate of GFT quanta. Finally, we sketch how the
proposal may be realised and its effective dynamics could be extracted in the
GFT setting and compared with continuum gravity theories.
