  This talk is inspired by two previous ICM talks, by V.Drinfeld (1986) and
G.Felder (1994). Namely, one of the main ideas of Drinfeld's talk is that the
quantum Yang-Baxter equation (QYBE), which is an important equation arising in
quantum field theory and statistical mechanics, is best understood within the
framework of Hopf algebras, or quantum groups. On the other hand, in Felder's
talk, it is explained that another important equation of mathematical physics,
the star-triangle relation, may (and should) be viewed as a generalization of
QYBE, in which solutions depend on additional ``dynamical'' parameters. It is
also explained there that to a solution of the quantum dynamical Yang-Baxter
equation one may associate a kind of quantum group. These ideas gave rise to a
vibrant new branch of ``quantum algebra'', which may be called the theory of
dynamical quantum groups. My goal in this talk is to give a bird's eye review
of some aspects of this theory and its applications.
