  We employ the framework of affine covariant quantization and associated
semiclassical portrait to address two main issues in the domain of quantum
gravitational systems: (i) the fate of singularities and (ii) the lack of
external time. Our discussion is based on finite-dimensional, symmetry-reduced
cosmological models. We show that the affine quantization of the cosmological
dynamics removes the classical singularity and univocally establishes a unitary
evolution. The semiclassical portrait based on the affine coherent states
exhibits a big bounce replacing the big-bang singularity. As a particularly
interesting application, we derive and study a unitary quantum dynamics of the
spatially homogenous, closed model, the Mixmaster universe. At the classical
level it undergoes an infinite number of oscillations before collapsing into a
big-crunch singularity. At the quantum level the singularity is shown to be
replaced by adiabatic and nonadiabatic bounces. As another application, we
consider the problem of time. We derive semiclassical portraits of quantum
dynamics of the Friedman universe with respect to various internal degrees of
freedom. Next we compare them and discuss the nature of quantum evolution of
the gravitational field.
