Beside their great successes, Cosmology and Particle Physics are facing deep issues that have been puzzling physicists for a long time. In particular, 85% of the matter content in our Universe is in the form a cold, non-interacting component, whose only impacts have been probed through gravity. On the other hand, the discovery of neutrino oscillations point towards the existence of tiny but non-vanishing neutrino masses, a phenomenon that cannot be successfully explained within the Standard Model of Particle Physics. This work tries to tackle the Dark Matter and neutrino masses canondrums, by looking for electromagnetic and gravitational signatures of peculiar massive relics onto Cosmological probes that have been developed over the years. In particular, we study the impact on i) CMB temperature and polarization anisotropies; ii) Large Scale Structure surveys; iii) Spectral distortions of the CMB blackbody spectrum; iv) and Big Bang Nucleosynthesis. After a thorough review of all necessary tools to compute those observables, we make use of the latest data from present experiments, and forecast the potential for detection of future ones. We firstly focus on the purely gravitational effects of a decaying massive relics, deriving the strongest constraints to date from the pure gravitational effects of the decay and extending the phenomenology to multicomponent models with very high decay rate. Those constraints represent robust, vastly model independent bounds that any massive relic has to satisfy. In a second step, we switch on electromagnetic channels and compare the relative constraining power of non-thermal Big Bang nucleosynthesis, CMB spectral distortions and statistics of CMB anisotropies. As an example, we apply our results to specific models taken from the literature, and show that a loophole to the standard theory of e.m. cascade allow to solve the cosmological Lithium problem thanks to photon injection. We then study the impact of annihilating relics, with a special emphasis on annihilations in halos and its synergy with stars in reionizing our Universe. The last part of this work is devoted to the cosmological determination of neutrino properties with current and future data. We assess that: i) it is possible to make a robust statement about the detection of the cosmic neutrino background by CMB experiments; ii) the joint analysis of future CMB and Large Scale Structure data should allow the first $5sigma$ Cosmological detection of neutrino masses. Our results emphasize the complementarity of the different probes, and the need for combined analyses when looking for new physics, especially in the era of precision Cosmology.
