This article presents a general overview of the problems involved in the application of the quantum principle to a theory of gravitation. The ultraviolet divergences that appear in any perturbative computation are reviewed in some detail, and it is argued that it is unlikely that any theory based on local quantum fields could be consistent. This leads in a natural way to a supersymmetric theory of extended objects as the next candidate theory to study. An elementary introduction to superstrings closes the review, and some speculations about the most promising avenues of research are offered.