  In this topical review we discuss the connections between chaos, decoherence
and quantum cosmology. We understand chaos as classical chaos in systems with a
finite number of degrees of freedom, decoherence as environment induced
decoherence and quantum cosmology as the theory of the Wheeler - DeWitt
equation or else the consistent history formulation thereof, first in mini
super spaces and later through its extension to midi super spaces. The overall
conclusion is that consideration of decoherence is necessary (and probably
sufficient) to sustain an interpretation of quantum cosmology based on the Wave
function of the Universe adopting a Wentzel - Kramers - Brillouin form for
large Universes, but a definitive account of the semiclassical transition in
classically chaotic cosmological models is not available in the literature yet.
