  We give, in some detail, a critical overview over recent work towards
deriving a cosmological phenomenology from the fundamental quantum dynamics of
group field theory (GFT), based on the picture of a macroscopic universe as a
"condensate" of a large number of quanta of geometry which are given by
excitations of the GFT field over a "no-space" vacuum. We emphasise conceptual
foundations, relations to other research programmes in GFT and the wider
context of loop quantum gravity (LQG), and connections to the quantum physics
of real Bose-Einstein condensates. We show how to extract an effective dynamics
for GFT condensates from the microscopic GFT physics, and how to compare it
with predictions of more conventional quantum cosmology models, in particular
loop quantum cosmology (LQC). No detailed familiarity with the GFT formalism is
assumed.
