  Proper group actions are ubiquitous in mathematics and have many of the
attractive features of actions of compact groups. In this survey, we discuss
proper actions of Lie groups on smooth manifolds. If the group dimension is
sufficiently high, all proper effective actions can be explicitly determined,
and our principal goal is to provide a comprehensive exposition of known
classification results in the complex setting. They include a complete
description of Kobayashi-hyperbolic manifolds with high-dimensional
automorphism group, which is a case of special interest.
