  We present a brief review on the Raychaudhuri equations. Beginning with a
summary of the essential features of the original article by Raychaudhuri and
subsequent work of numerous authors, we move on to a discussion of the
equations in the context of alternate non--Riemannian spacetimes as well as
other theories of gravity, with a special mention on the equations in
spacetimes with torsion (Einstein--Cartan--Sciama--Kibble theory). Finally, we
give an overview of some recent applications of these equations in General
Relativity, Quantum Field Theory, String Theory and the theory of relativisitic
membranes. We conclude with a summary and provide our own perspectives on
directions of future research.
