In very recent times, a new major issue has arisen: Is the true story of the very distant galactic motions, that is in terms of the universe as a whole, the one that had been assumed? Is it simply a matter of gravity slowing down the expansion of the universe? It certainly seems reasonable. However in more recent years, data has been presented to suggest (and most recently claimed to affirm) that rather than slowing down, the expansion of the universe is actually speeding up! This data comes from the observations of certain supernovae, massive exploding stars in distant galaxies. The observations of these distant supernovae are dimmer than they would have to be on the basis of a universe that is decelerating in the course of its expansion. Instead, the currently favoured view is that the universe is now undergoing an expansion with acceleration. This runs counter to our fundamental experience with gravitation, that gravity attracts rather than repels, the latter going hand-in-hand with acceleration accompanying the expansion.