  This is the extended version of a survey prepared for publication in the
Springer INdAM series.
  Superbosonisation, introduced by Littelmann-Sommers-Zirnbauer, is a
generalisation of bosonisation, with applications in Random Matrix Theory and
Condensed Matter Physics. We link the superbosonisation identity to
Representation Theory and Harmonic Analysis and explain two new proofs, one via
the Laplace transform and one based on a multiplicity freeness statement.
