  Loop quantum cosmology is an application of recent developments for a
non-perturbative and background independent quantization of gravity to a
cosmological setting. Characteristic properties of the quantization such as
discreteness of spatial geometry entail physical consequences for the structure
of classical singularities as well as the evolution of the very early universe.
While the singularity issue in general requires one to use difference equations
for a wave function of the universe, phenomenological scenarios for the
evolution are based on effective equations implementing the main quantum
modifications. These equations show generic bounces as well as inflation in
diverse models, which have been combined to more complicated scenarios.
