  Quillen showed how to describe the homotopy theory of simply-connected
rational spaces in terms of differential graded Lie algebras. Here we survey a
generalization of Quillen's results that describes the $v_n$-periodic
localizations of homotopy theory (where rational corresponds to $n=0$) in terms
of spectral Lie algebras. The latter form an extension of the theory of Lie
algebras to the setting of stable homotopy theory. This is a chapter written
for the Handbook of Homotopy Theory edited by Haynes Miller.
