  This is the full text of a survey talk for nonspecialists, delivered at the
66th Annual Meeting of the German Physical Society in Leipzig, March 2002. We
have not taken pains to suppress the colloquial style. References are given
only insofar as they help to underline the points made; this is not a
full-blooded survey. The connection between noncommutative field theory and
string theory is mentioned, but deemphasized. Contributions to noncommutative
geometry made in Germany are emphasized.
