The direct detection of light dark matter particles with traditional experiments is challenging, due to the expected small energy depositions at Earth-based detectors. In this talk, I will first summarize a variety of scenarios in which light dark matter could be directly probed with current technologies, by making use of the Migdal effect and a small fraction of high-speed dark matter particles reaching the detector. Then, I will discuss how light dark matter may also cool protons, electrons, neutrinos and photons in the vicinity of some supermassive black holes in Active Galactic Nuclei. This new phenomenological indirect probe allows to set strong constraints on the parameter space of light dark matter, competitive with complementary constraints from direct detection experiments and cosmology. We will demonstrate that thermal and non-thermal dark matter models are already being probed with current multi-messenger observations from Active Galactic Nuclei.