  In this paper I present a brief survey of the active area of Special
Functions associated with Root Systems. The article is intended for a general
mathematical audience. It will not suppose prerequisites on either special
functions or root systems. It will also skip many technical details. Some early
work in this area (root systems BC_2 and A_2) was done by the author [17] and
Sprinkhuizen [32]. During the last ten years important breakthroughs were made
by Heckman and Opdam [11], [27], [28], [12], Macdonald [23], [24], Dunkl [8]
and Cherednik [3], [4], [5].
