Symmetric solutions and related models present some of the main methods to extract physical information from classical or quantum gravity. Several techniques to construct representative models have been developed for one of the current candidates for a quantum theory of gravity, loop quantum gravity. For realistic situations, which are never exactly symmetric, more general formulations containing at least small values of general fields such as inhomogeneities will be developed. This is essential for, e.g., predictions in cosmological observations or to understand properties of black holes. An analysis of the resulting equations will be carried out in order to arrive at consistency tests of the general framework as well as possible observable effects. Since quantum theories of gravity are still being developed, any information on the behavior of possible candidates, in particular in physical scenarios, will help to lead the theoretical construction. Quantum gravity, in turn, is widely believed to be essential for the understanding of the universe at a fundamental level. This applies in particular to the two main areas of applications, cosmology and black holes, which receive wide interest in the general public. Models as developed here allow the development of intuitive explanations which make such a broad dissemination possible. In simplifying the complex full theories, suitable models also provide ideal entry points for students or researchers new to the field.
