Loop quantum cosmology attempts to understand the full dynamics of loop quantum gravity by realizing crucial effects in simpler, usually symmetric settings. Several subtleties arise especially when cosmological questions are to be addressed, related to possible mini-superspace artefacts, consistent cosmological perturbation theory, and quantum space-time structure. Recent work on inhomogeneous perturbations has highlighted some of the dangers of an over-reliance on simple models, sometimes not just reduced by symmetry but also in the possible forms of matter or quantum corrections. Only a consistent treatment of inhomogeneity, taking into account the full gauge structure related to general covariance, can show what happens at high densities in quantum gravity. The relevant methods and results (especially effective equations, potential observational signatures, singularity resolution and signature change) are surveyed in here.