“The discrepancy between what was expected and what has been observed has grown over the years, and we’re straining harder and harder to fill the gap.” –Jeremiah P. Ostriker
When it comes to the Universe, and the structure in it, from galaxies to groups to clusters to the grand cosmic web on the largest scales, you simply can’t account for it all without dark matter.
But in principle, you might not need dark matter to do it; you might be able to modify the laws of gravity instead to take care of it. Imagine a Universe devoid of dark matter, but where a new theory of gravity could account for all the observations we see. This idea — called MOND in general (for MOdified Newtonian Dynamics) — has been dark matter’s leading competitor. Just a decade ago, a relativistic formulation of MOND known as TeVeS became all the rage.
And thanks to new observations, TeVeS has been refuted! Go read the whole thing.