  We survey the topology which led to the original bar and cobar constructions,
for both associative algebras and coalgebras and for Lie algebras and
commutative coalgebras. These constructions are often viewed as part of the
larger theory of Koszul duality of operads, so this survey is meant to offer an
historical perspective on the most prominent cases of that theory. We also
explain recent work which shows that Hopf/linking invariants for homotopy are
at the heart of the duality between commutative algebras and Lie coalgebras.
