We first present the phenomenological successes of the Modified Newtonian Dynamics (MOND) paradigm on galaxy scales, as well as its problems on subgalactic and extragalactic scales, together with possible solutions. We then show that the the covariant modified gravity theories proposed so far, successful at reproducing the MOND phenomenology in galaxies, mostly have to replace the concept of "dark matter" by the concept of "dark fields".