The Large-Scale Smoothness of the Universe

New measurements of galaxy clustering and background radiations provide improved constraints on the isotropy and homogeneity of the Universe on large scales. In particular, the angular distribution of radio sources and the X-Ray Background probe density fluctuations on scales intermediate between those explored by galaxy surveys and the Cosmic Microwave Background experiments. On a scale of $\sim 100 \Mpc$ the rms density fluctuations are at the level of $\sim 10%$ and on scales larger than $300 \Mpc$ the distribution of both mass and luminous sources safely satisfies the `Cosmological Principle' of isotropy and homogeneity. The transition with scale from clumpiness to homogeneity can be phrased in terms of the fractal dimension of the galaxy and mass distributions.