  This paper surveys eight classes of polynomials associated with $A$-type and
$BC$-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and
interpolation (or shifted) Jack and Macdonald polynomials and their $BC$-type
extensions. Among these the $BC$-type interpolation Jack polynomials were
probably unobserved until now. Much emphasis is put on combinatorial formulas
and binomial formulas for (most of) these polynomials. Possibly new results
derived from these formulas are a limit from Koornwinder to Macdonald
polynomials, an explicit formula for Koornwinder polynomials in two variables,
and a combinatorial expression for the coefficients of the expansion of
$BC$-type Jacobi polynomials in terms of Jack polynomials which is different
from Macdonald's combinatorial expression. For these last coefficients in the
two-variable case the explicit expression in Koornwinder & Sprinkhuizen (1978)
is now obtained in a quite different way.
