Michel Coste Université de Rennes I In semialgebraic and o-minimal geometry there are many results of finiteness and trivialization in families. One of the most important is Hardt's theorem asserting that a semialgebraic family is trivial after a finite partition of the parameter space. I intend to present the method of ideal points which is a tool for the study of families, and allows for instance to obtain Hardt's theorem almost immediately from a triangulation theorem.