How smooth is the Universe on large scales?

New measurements of galaxy clustering and background radiations can provide improved constraints on the isotropy and homogeneity of the Universe on scales larger than 100 $h^{-1}$ Mpc. 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 Cosmic Microwave Background experiments. On scales larger than 300 $h^{-1}$ Mpc the distribution of both mass and luminous sources satisfies well the `Cosmological Principle' of isotropy and homogeneity. Although the fractal dimension of the galaxy distribution on scales $\lta 20 \Mpc$ is $D_2 \approx 1.2-2.2$, the fluctuations in the X-ray Background and in the Cosmic Microwave Background are consistent with $D_2=3$ to within $10^{-4}$ on the very large scales. We also discuss limits on non-Gaussian fluctuations.