  In this thesis, we study the implications of Quantum Gravity models for the
dynamics of spacetime and the ensuing departures from classical General
Relativity. The main focus is on cosmological applications, particularly the
impact of quantum gravitational effects on the dynamics of a homogenous and
isotropic cosmological background. Our interest lies in the consequences for
the evolution of the early universe and singularity resolution, as well as in
the possibility of providing an alternative explanation for dark matter and
dark energy in the late universe.
  The thesis is divided into two main parts, dedicated to alternative (and
complementary) ways of tackling the problem of Quantum Gravity. The first part
is concerned with cosmological applications of background independent
approaches to Quantum Gravity, both in the context of loop quantisation and in
quantum geometrodynamics. Particularly relevant in this work is the Group Field
Theory approach, which we use to study the effective dynamics of the emergent
universe from a full theory of Quantum Gravity (i.e. without symmetry
reduction).
  In the second part, modified gravity theories are introduced as tools to
provide an effective description of quantum gravitational effects, e.g. by
introducing new degrees of freedom and symmetries. Particularly relevant in
this respect is local conformal invariance, which finds a natural realisation
in the framework of Weyl geometry. We build a modified theory of gravity based
on such symmetry principle, and argue that new fields in the extended
gravitational sector may play the role of dark matter. New degrees of freedom
are also natural in models with varying fundamental `constants', which we
examine critically.
  Finally, we discuss prospects for future work and point at directions for the
derivation of realistic cosmological models from Quantum Gravity candidates.
