  As first discovered by Choptuik, the black hole threshold in the space of
initial data for general relativity shows both surprising structure and
surprising simplicity. Universality, power-law scaling of the black hole mass,
and scale echoing have given rise to the term ``critical phenomena''. They are
explained by the existence of exact solutions which are attractors within the
black hole threshold, that is, attractors of codimension one in phase space,
and which are typically self-similar. This review gives an introduction to the
phenomena, tries to summarize the essential features of what is happening, and
then presents extensions and applications of this basic scenario. Critical
phenomena are of interest particularly for creating surprising structure from
simple equations, and for the light they throw on cosmic censorship and the
generic dynamics of general relativity.
