  We briefly review various mappings of fermion pairs to bosons, including
those based on mapping operators, such as Belyaev-Zelevinskii, and those on
mapping states, such as Marumori; in particular we consider the work of
Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then
give a rigorous and unified description of state-mapping procedures which
allows one to systematically go beyond Otsuka-Arima-Iachello and related
approaches, along with several exact results.
