  Aspects of the full theory of loop quantum gravity can be studied in a
simpler context by reducing to symmetric models like cosmological ones. This
leads to several applications where loop effects play a significant role when
one is sensitive to the quantum regime. As a consequence, the structure of and
the approach to classical singularities are very different from general
relativity: The quantum theory is free of singularities, and there are new
phenomenological scenarios for the evolution of the very early universe
including inflation. We give an overview of the main effects, focussing on
recent results obtained by several different groups.
