  Recently there has been a renewed interest in an extension of the notion of
orthogonal polynomials known as multiple orthogonal polynomials. This notion
comes from simultaneous rational approximation (Hermite-Pade approximation) of
a system of several functions. We describe seven families of multiple
orthogonal polynomials which have he same flavor as the very classical
orthogonal polynomials of Jacobi, Laguerre and Hermite. We also mention some
open research problems and some applications.
