  The Koszul homology algebra of a commutative local (or graded) ring $R$ tends
to reflect important information about the ring $R$ and its properties. In
fact, certain classes of rings are characterized by the algebra structure on
their Koszul homologies. In this paper we survey some classical results on the
Koszul homology algebras of such rings and highlight some applications. We
report on recent progress on the Koszul homology algebras of Koszul algebras
and examine some open questions on the topic.
