By the time, in 1937, the Swiss astronomer Zwicky measured the velocity dispersion of the Coma cluster of galaxies, astronomers somehow got acquainted with the idea that the universe is filled by some kind of dark matter. After almost a century of investigations, we have learned two things about dark matter, (i) it has to be non-baryonic -- that is, made of something new that interact with normal matter only by gravitation-- and, (ii) that its effects are observed in stellar systems when and only when their internal acceleration of gravity falls below a fix value a0=1.2x10-8 cm s-2. This systematic, more than anything else, tells us we might be facing a failure of the law of gravity in the weak field limit rather then the effects of dark matter. Thus, in an attempt to avoid the need for dark matter, the Modified Newtonian Dynamics. MOND posits a breakdown of Newton's law of gravity (or inertia) below a0, after which the dependence with distance became linear. Despite many attempts, MOND resisted stubbornly to be falsified as an alternative to dark matter and succeeds in explaining the properties of an impressively large number of objects without invoking the presence of non-baryonic dark matter. In this paper, I will review the basics of MOND and its ability to explain observations without the need of dark matter.

To Appear in the proceeding of the "First crisis in cosmology" conference, published in the American Institute of Physiscs' proceedings series, Vol. 822. (includes 13 pages and 12 figures)