Cosmological models that invoke warm or cold dark matter can not explain observed regularities in the properties of dwarf galaxies, their highly anisotropic spatial distributions, nor the correlation between observed mass discrepancies and acceleration. These problems with the standard model of cosmology have deep implications, in particular in combination with the observation that the data are excellently described by Modified Newtonian Dynamics (MOND). MOND is a classical dynamics theory which explains the mass discrepancies in galactic systems, and in the universe at large, without invoking dark entities. MOND introduces a new universal constant of nature with the dimensions of acceleration, a0, such that the pre-MONDian dynamics is valid for accelerations a >> a0, and the deep MONDian regime is obtained for a << a0, where space-time scale invariance is invoked. Remaining challenges for MOND are (i) explaining fully the observed mass discrepancies in galaxy clusters, and (ii) the development of a relativistic theory of MOND that will satisfactorily account for cosmology. The universal constant a0 turns out to have an intriguing connection with cosmology: bar a0 == 2 pi a0 approx c H_0 approx c^2(Lambda/3)^{1/2}. This may point to a deep connection between cosmology and internal dynamics of local systems.
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