  Any spacetime containing a degenerate Killing horizon, such as an extremal
black hole, possesses a well-defined notion of a near-horizon geometry. We
review such near-horizon geometry solutions in a variety of dimensions and
theories in a unified manner. We discuss various general results including
horizon topology and near-horizon symmetry enhancement. We also discuss the
status of the classification of near-horizon geometries in theories ranging
from vacuum gravity to Einstein-Maxwell theory and supergravity theories.
Finally, we discuss applications to the classification of extremal black holes
and various related topics. Several new results are presented and open problems
are highlighted throughout.
