Optimal Lipschitz extensions

The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces(X,dX)and(Y,dY)such that for all Ω ⊂ X and for all Lipschitz function and for all Lipschitz functionf : Ω → Y, then there is a functiong : X → Ythat extendsfand has the same Lipschitz constant asf. In this paper we discuss some results and open questions related to that issue.