The distribution of the non-luminous matter in galaxies of different luminosity and Hubble type is much more than a proof of the existence of dark particles governing the structures of the Universe. Here, we will review the complex but well-ordered scenario of the properties of the dark halos also in relation with those of the baryonic components they host. Moreover, we will present a number of tight and unexpected correlations between selected properties of the dark and the luminous matter. Such entanglement evolves across the varying properties of the luminous component and it seems to unequivocally lead to a dark particle able to interact with the Standard Model particles over cosmological times. This review will also focus on whether we need a paradigm shift, from pure collisionless dark particles emerging from "first principles", to particles that we can discover only by looking to how they have designed the structure of the galaxies. \keywords{Dark matter \and Galaxies \and Cosmology \and Elementary particles}

60 pages, 28 Figures ~220 refs. Invited review for The Astronomy and Astrophysics Review. It matches the published version