Contrary to popular belief, on very large distance scales visible matter stubbornly refuses to "fall" according to the laws of gravity of both Newton and Einstein. The paradox has led to the introduction of dark matter, purporting to explain the observed surplus of gravitational pull. The logical possibility remains that there is no dark matter, what you see is all there is, and that the paradox simply signals the break down of the Einstein-Newton theory of gravity. I will review alternative theories of gravity that do away with the need for dark matter. Surprisingly Solar system gravitational experiments, such as those associated with the LISA Pathfinder mission, might settle the score between the two approaches.