A glimpse on Dark Matter particles shining through the gamma-ray sky

In an era of unprecedented sensitivity to cosmic gamma rays, it is timely to study possible signatures rising from Dark Matter (DM) particle interactions. The aim of the present thesis is precisely devoted to that. We start by presenting a broad study on physically motivated Galactic diffuse emission models. These derive from the interaction of Galactic cosmic rays with the interstellar medium and describe the bulk of photons imprinted in the observed gamma-ray sky. We show how gamma-ray data offer a complementary deep diagnostic of the standard paradigm for Galactic cosmic-ray propagation, usually tuned on local cosmic-ray observables. We present a self-contained discussion about the inferred radial gradients in the gamma-ray data relative to the Galactic plane region, and interpret them as a strong hint in favor of a spatially varying diffusion rate for cosmic rays in the Galaxy. We corroborate this study with a set of distinctive predictions, embracing the available information on TeV high-energy photon data and the expectations for a detection of Galactic neutrino fluxes on the basis of current and future neutrino observatory sensitivities. We, then, scrutinize the claim of a gamma-ray signal from DM particle annihilation observed in the innermost central part of our Galaxy, analyzing the gamma-ray data coming from few tens of degrees around the Galactic center. We show that a spherical excess -- interpretable as the annihilation of weakly interacting massive particles in the Galactic halo -- does not stand out in the data any longer when the effect of the observationally inferred high star-formation rate in this complex astrophysical environment is considered. Accounting properly for that in the injection source distribution of cosmic rays, we show that most of the "GeV excess" has a simple explanation in terms of well-motivated cosmic-ray physics. We remark, in particular, that with this correction, counts in the residual map are not only drastically reduced, but also do not spatially correlate anymore with an approximately spherical morphology. Finally, we critically reassess the DM content in the satellites of the Milky Way. In order to do that, we develop a new method, mainly based on the kinematics of the stars in these galaxies, that in the end provides a conservative estimate of the line-of-sight integrated halo profile squared for these objects, the so-called J-factor. After carrying out in detail the study case of Ursa Minor, we present here -- as last original contribution in the thesis -- a similar conservative analysis of the J-factor for the whole set of classical satellites of the Milky Way. In light of our novel approach, we conclude that these galaxies offer to us a reliable "DM laboratory" where we can probe the freeze-out mechanism of cold thermal relics in a robust and unique way.