Inflation predicts that the Universe is homogeneous and isotropic---that is, it is the same everywhere and in every direction.  Cosmological homogeneity and isotropy are generally *assumed* to be true, but this is a prediction that can be tested quantitatively.  I will first discuss some new tests of statistical homogeneity and isotropy, and related tests for a preferred cosmological frame.  I will then review briefly some recent evidence that may show a departure from homogeneity and present a theoretical model that may account for this anomaly.  In the last few minutes, I may speculate wildly about the pre-inflationary Universe.