  This thesis treats the topic of CMB Spectral Distortions (SDs), which
represent any deviation from a pure black body shape of the CMB energy
spectrum. As such, they can be used to probe the inflationary, expansion and
thermal evolution of the universe both within $\Lambda$CDM and beyond it. The
currently missing observation of this rich probe of the universe makes of it an
ideal target for future observational campaigns. In fact, while the
$\Lambda$CDM signal guarantees a discovery, the sensitivity to a wide variety
of new physics opens the door to an enormous uncharted territory. In light of
these considerations, the thesis opens by reviewing the topic of CMB SDs in a
pedagogical and illustrative fashion, aimed at waking the interest of the
broader community. This introductory premise sets the stage for the first main
contribution of the thesis to the field of SDs: their implementation in the
Boltzmann solver CLASS and the parameter inference code MontePython. The
CLASS+MontePython pipeline is publicly available, fast, it includes all sources
of SDs within $\Lambda$CDM and many others beyond that, and allows to
consistently account for any observational setup. By means of these numerical
tools, the second main contribution of the thesis consists in showcasing the
versatility and competitiveness of SDs for several cosmological models as well
as for a number of different mission designs. Among others, the results cover
features in the primordial power spectrum, primordial gravitational waves,
non-standard dark matter properties, primordial black holes, primordial
magnetic fields and Hubble tension. Finally, the manuscript is disseminated
with (20) follow-up ideas that naturally extend the work carried out so far,
highlighting how rich of unexplored possibilities the field of CMB SDs still
is. The hope is that these suggestions will become a propeller for further
interesting developments.
