  The classical Schur polynomials form a natural basis for the ring of
symmetric polynomials, and have geometric significance since they represent the
Schubert classes in the cohomology ring of Grassmannians. Moreover, these
polynomials enjoy rich combinatorial properties. In the last decade, an exact
analogue of this picture has emerged in the symplectic and orthogonal Lie
types, with the Schur polynomials replaced by the theta and eta polynomials of
Buch, Kresch, and the author. This expository paper gives an overview of what
is known to date about this correspondence, with examples.
