  Quantum cosmology has traditionally been studied at the level of
symmetry-reduced minisuperspace models, analyzing the behavior of wave
functions. However, in the absence of a complete full setting of quantum
gravity and detailed knowledge of specific properties of quantum states, it
remained difficult to make testable predictions. For quantum cosmology to be
part of empirical science, it must allow for a systematic framework in which
corrections to well-tested classical equations can be derived, with any
ambiguities and ignorance sufficiently parameterized. As in particle and
condensed-matter physics, a successful viewpoint is one of effective theories,
adapted to specific issues one encounters in quantum cosmology. This review
presents such an effective framework of quantum cosmology, taking into account,
among other things, space-time structures, covariance, the problem of time and
the anomaly issue.
