This paper presents a survey of recent results in the theory of rational sets in arbitrary monoids. Main topics considered here are : the so-called Kleene monoids (i.e. monoids where Kleene's theorem holds), rational functions and relations, rational sets in partially commutative monoids, and rational sets in free groups.
This work has been partly supported by the Programme de Recherche Coordonnée "Mathématiques et Informatique" du Ministère de la Recherche et de la Technologie.