Lagrange interpolation on the semiaxis. A survey

In this brief survey are collected some recent results about optimal interpolation processes of Lagrange type based on the zeros of {it generalized Laguerre polynomials}, i.e. the sequence of orthogonal polynomials ${p_m(w_alpha)}_m$ where $w_alpha(x)=e^{-x^eta}x^alpha.$ A new extended Lagrange process having optimal Lebesgue constants is also introduced.