  Recent results on the Grassmannian perspective of soliton equations with an
elliptic spectral parameter are presented along with a detailed review of the
classical case with a rational spectral parameter. The nonlinear Schr\"odinger
hierarchy is picked out for illustration of the classical case. This system is
formulated as a dynamical system on a Lie group of Laurent series with
factorization structure. The factorization structure induces a mapping to an
infinite dimensional Grassmann variety. The dynamical system on the Lie group
is thereby mapped to a simple dynamical system on a subset of the Grassmann
variety. Upon suitable modification, almost the same procedure turns out to
work for soliton equations with an elliptic spectral parameters. A clue is the
geometry of holomorphic vector bundles over the elliptic curve hidden (or
manifest) in the zero-curvature representation.
