  We discuss the hints for the disappearance of continuum space and time at
microscopic scale. These include arguments for a discrete nature of them or for
a fundamental non-locality, in a quantum theory of gravity. We discuss how
these ideas are realized in specific quantum gravity approaches. Turning then
the problem around, we consider the emergence of continuum space and time from
the collective behaviour of discrete, pre-geometric atoms of quantum space, and
for understanding spacetime as a kind of "condensate", and we present the case
for this emergence process being the result of a phase transition, dubbed
"geometrogenesis". We discuss some conceptual issues of this scenario and of
the idea of emergent spacetime in general. As a concrete example, we outline
the GFT framework for quantum gravity, and illustrate a tentative procedure for
the emergence of spacetime in this framework. Last, we re-examine the
conceptual issues raised by the emergent spacetime scenario in light of this
concrete example.
