  In the last decade, progress on quantization of homogeneous cosmological
spacetimes using techniques of loop quantum gravity has led to insights on
various fundamental questions and has opened new avenues to explore Planck
scale physics. These include the problem of singularities and their possible
generic resolution, constructing viable non-singular models of the very early
universe, and bridging quantum gravity with cosmological observations. These
results, which emerge from an interplay of sophisticated analytical and
numerical techniques, has also led to valuable hints on loop quantization of
black hole and inhomogeneous spacetimes. In this review, we provide a summary
of this progress while focusing on concrete examples of the quantization
procedure and phenomenology of cosmological perturbations.
