In the most recent studies on language processing the role of the right hemisphere has been the object of renewed attention, in a series of works aimed at underlining its role in pragmatic processing as well as in various tasks previously attributed to the sole left hemisphere. This paper presents a brief review of the latest studies on the role of the right hemisphere in the so-called normal language processing, that is in the processing of the language spoken by right-handed subjects not suffering from language pathologies, with particular reference to pragmatic processing and to a series of aspects related to lexical-semantic processing, in the perspective of highlighting some critical issues of the matter and outline a sort of research program on the right hemisphere contribution to language processing.