Approximating a function with rational interpolation often
gives excellent results, but it is generally hard to control
the occurrence of poles. However, the particular class of
barycentric rational interpolants is guaranteed to have no
poles and arbitrarily high approximation power. We first
give an introduction to this kind of interpolation and then
study the corresponding Lebesgue constants, which turn out
to have logarithmic growth in the case of equidistant
interpolation points.

[Invited by J-P.Berrut]