  The occurrence of singularities where spacetime curvature becomes infinite
and geodesic evolution breaks down are inevitable events in classical general
relativity (GR) unless one chooses an exotic matter violating weak energy
condition. These singularities show up in various physical processes, such as
the gravitational collapse, the birth of the universe in the standard cosmology
as well as the classical solutions of the black hole spacetimes. In the last
two decades, a rigorous understanding of the dynamics of quantum spacetime and
the way it resolves singularities has been achieved in loop quantum cosmology
(LQC) which applies the concepts and techniques of loop quantum gravity to the
symmetry reduced cosmological spacetimes. Due to the fundamental discreteness
of quantum geometry derived from the quantum theory, the big bang singularity
has been robustly shown to be replaced by a big bounce. Strong curvature
singularities intrinsic in the classical cosmology are generically resolved for
a variety of cosmological spacetimes including anisotropic models and polarized
Gowdy models. Using effective spacetime description the LQC universe also
provides an ultra-violet complete description of the classical inflationary
scenario as well as its alternatives such as the ekpyrotic and matter bounce
scenarios. In this chapter we provide a summary of singularity resolution and
its physical implications for various isotropic and anisotropic cosmological
spacetimes in LQC and analyze robustness of results through variant models
originating from different quantization prescriptions.
