Titolo: An update on the semantics of lambda-calculus Autore: F. Honsell Abstract: We shall present various results and open questions on the F-completeness of various classes af models of untyped lambda-calculus. We recall that if M' included in M are two classes of lambda-models, and F is a class of formulae, M' is F-complete w.r.t. M if, for every formula Phi in F, whenever all the models in M' satisfy Phi, all the models in M satisfy Phi too. If time permits, we shall present some elementary uses of pre-logical relations to models of polymorphism.