The most compelling candidates for Dark Matter to day are WIMPs and axions. The applicability of gasesous Time Projection Chambers (TPCs) with Micromesh Gas Structures (Micromegas) to the search of these particles is explored within this work. Both particles would produce an extremely low rate at very low energies in particle detectors. Micromegas detectors can provide both low background rates and low en- ergy threshold, due to the high granularity, radiopurity and uniformity of the readout. Small (few cm wide) Micromegas detectors are used to image the axion-induced x-ray signal expected in the CERN Axion Solar Telescope (CAST) experiment. We show the background levels obtained in CAST and the prospects to further reduce them to the values required by the Internation Axion Observatory (IAXO). We also present TREX-DM, a scaled-up version of the Micromegas used in axion research, but this time dedicated to the low-mass WIMP detection. TREX-DM is a high-pressure Micromegas-based TPC designed to host a few hundreds of grams of light nuclei (argon or neon) with energy thresholds potentially at the level of 100 eV. The detector is described in detail, as well as the results of the commissioning and characterization phase on surface. Besides, the back- ground model of TREX-DM is presented, along with the anticipated sensitivity of this search, which could go beyond current experimental limits.
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