Hari Kunduri and James Lucietti
Any spacetime containing a degenerate horizon 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, Einstein--Maxwell theory and supergravity theories. An emphasis is placed on applications to extremal black holes. Several new results are presented and open problems are highlighted throughout.