  Our review is devoted to three promising research lines in quantum cosmology
and the physics of the early universe. The nonperturbative renormalization
programme is making encouraging progress that we here assess from the point of
view of cosmological applications: Lagrangian and Hamiltonian form of pure
gravity with variable G and Lambda; power-law inflation for pure gravity; an
accelerating universe without dark energy. In perturbative quantum cosmology,
on the other hand, diffeomorphism-invariant boundary conditions lead naturally
to a singularity-free one-loop wave function of the universe. Last, but not
least, in the braneworld picture one discovers the novel concept of
cosmological wave function of the bulk space-time. Its impact on quantum
cosmology and singularity avoidance is still, to a large extent, unexplored.
