  This extensive survey is an invited contribution to the Encyclopedia of
Mathematical Physics, 2nd edition. It covers both classical and more modern
aspects of configuration spaces of points on a "ground space" $M$. Most results
pertain to $M$ a manifold. Configuration spaces of points have become so
omnipresent in so many areas of mathematics, physics, and even the applied
sciences, that a survey can only cover a selection of topics. We review key
ideas, constructions, and results.
