We discuss the existence of an acceleration scale in galaxies and galaxy clusters. The presence of the same acceleration scale found at very different scales and in very different astrophysical objects strongly supports the existence of a fundamental acceleration scale governing the observed gravitational physics. We also comment on the implication of such a fundamental acceleration scale on the problem of dark matter. We discuss the relevance of the fundamental acceleration for the nature of dark matter as well as for structure formation to be explored in future numerical simulations.