How Smooth is the Universe on Large Scales ?

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We review cosmological inference from optical and radio galaxy surveys, the X-Ray Background and the Cosmic Microwave Background. We focus on three topics: (i) First results from the 2dF galaxy redshift survey; (ii) Estimation of cosmological parameters by joint analysis of redshift surveys and CMB data; and (iii) The validity of the Cosmological Principle, and constraints on the fractal dimension on large scales.
Invited talk, to appear in the Proceedings of the 49th Yamada conference on `Black Holes and High Energy Astrophysics', held in Kyoto in April 1998, in honour of Prof. H. Sato, 11 pages, 4 ps figures (Latex, black.sty, holes.sty)

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