  This paper consists of two (still only vaguely) related parts: in the first,
we briefly review work done in the past three years on the ``planar
equivalence" between a class of non-supersymmetric theories (including limiting
cases of QCD) and their corresponding supersymmetric "parents"; in the second,
we present details of a new formulation of planar quantum mechanics and
illustrate its effectiveness in an intriguing supersymmetric example.
