Gravitational evidences at diferent cosmological scales hint towards the existence of a dark component of the Universe, which amounts up to the 85% of its matter density. Despite all the eforts, the dark matter (DM) has eluded any clear detection and its ultimate nature remains still unknown. The current knowledge suggests that the DM cannot be identifed with the particles comprised in the Standard Model (SM). In this context, the Weakly Interacting Massive Particles (WIMPs) provide a framework that naturally yields the measured DM relic density, while at the same time they are expected to interact with SM particles. From these interactions, one of the most promising channels are γ-rays, which travel the Universe without defection, pointing back towards its original source. This Thesis has been devoted to unveil the unknown properties of the dark matter focusing on the so-called γ-ray indirect DM searches. We have conducted an exhaustive study of the DM contents and distribution in diferent interesting astrophysical objects and computed the state-of-the-art predictions for their annihilation and decay DM fuxes. Then, we have used these models to both, perform searches in existing F ermi-LAT data and obtain the prospects for the future Cherenkov Telescope Array (CTA). In the absence of detection, we proceed to a systematic search starting with galaxy clusters, known to be very good candidates to search DM emission. We compute the sensitivity to difuse γ-ray emission from Perseus, one of the most massive local galaxy clusters, of the future CTA, including in the analysis the CR-induced γ-rays as a background in a template ftting analysis. Staying with galaxy clusters, we then use 12 years of Fermi-LAT data from nearly 50 local galaxy clusters, searching for a DM-induced γ-ray signal, modelled including the expected substructures. We also explore introducing new targets in the quest of DM. For this, we perform the frst DM γ-ray search in dwarf irregular galaxies (dIrrs) using Fermi-LAT data. Finally, we collect the results of the previous studies to model the DM content of a subsample of objects that we have already investigated (dIrrs and clusters) and also of representative dark subhalos of the Milky Way
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