  This paper gives a survey of recent progress in isoparametric functions and
isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric
functions on Riemannian manifolds, including exotic spheres. The existences and
non-existences will be considered. (2) The Yau conjecture on the first
eigenvalues of the embedded minimal hypersurfaces in the unit spheres. The
history and progress of the Yau conjecture on minimal isoparametric
hypersurfaces will be stated.
