  The cosmic microwave background (CMB) is a relic radiation of the Big Bang
and as such it contains a wealth of cosmological information. Statistical
analyses of the CMB, in conjunction with other cosmological observables,
represent some of the most powerful techniques available to cosmologists for
placing strong constraints on the cosmological parameters that describe the
origin, content and evolution of the Universe. The last decade has witnessed
the introduction of wavelet analyses in cosmology and, in particular, their
application to the CMB. We review here spherical wavelet analyses of the CMB
that test the standard cosmological concordance model. The assumption that the
temperature anisotropies of the CMB are a realisation of a statistically
isotropic Gaussian random field on the sphere is questioned. Deviations from
both statistical isotropy and Gaussianity are detected in the reviewed works,
suggesting more exotic cosmological models may be required to explain our
Universe. We also review spherical wavelet analyses that independently provide
evidence for dark energy, an exotic component of our Universe of which we know
very little currently. The effectiveness of accounting correctly for the
geometry of the sphere in the wavelet analysis of full-sky CMB data is
demonstrated by the highly significant detections of physical processes and
effects that are made in these reviewed works.
