The Special Theory of Relativity, we teach our students, did away with Absolute Space and Absolute Time, leaving us with no absolute motion or rest, and also no absolute time order. General Relativity is viewed as extending the "relativity of motion" applicable to curved spacetimes, and General Relativity's most probable models of our actual spacetimes (the big-bang models) appear to re-introduce a privileged "cosmic" time order, and a definite sense of absolute rest. In particular, some of the same kinds of effects whose *absence* led to rejection of Newtonian absolute space are present in these models of GTR.