If the twentieth century can be characterized by the development of two main trends of formal grammars (-namely, Chomkyan’s grammars and Categorial Grammars), it is a fact that the present century is distinguished by the survival of only one formal paradigm (since Chomsky has himself contributed to destroy his own approach). The remaining categorial perspective takes root in a classical conception of linguistics (where the categories are derived from the traditional parts of speech), but has the aim of implementing the syntax and the semantic of natural languages thanks to a universal algebraic notation. In order to do that, the difficulty is to overcome the problems due to overgeneration and undergeneration which respectively intervene when grammar classifies certain expressions as derivable while in fact they are ill-formed or fails to provide the means to derive certain well-formed expressions. This difficulty encountered by every grammar is more acute in the case of categorial grammars and is a true challenge, because categorial grammars are their expressive capabilities limited to those of context-free grammars. According to Chomsky (1957), Categorial grammars’ theoreticians are aware of this main flaw, since they agree with Moortgat’s statement that « Natural languages exhibit structural patterns that require analytical tools stronger than context-free » (2002). The aim of this communication is to compare three contemporary categorial grammars (-the pregroup grammar, -the multimodal type-logics, and the non-commutative linear logic) that have roots in Lambek’s original type calculus (1958). In a first time, I will point out the empirical facts which are unsolvable by categorial approach. This study will allow to set up the challenges and the perspectives of current categorial grammars. Then, in a second time, I will analyze the strategies developed by these three formalisms to achieve the required extra expressivity. This critical survey will give raise to a meta-theoretical querying concerning the psychological and semantical relevance of this kind of formal grammar. So, we will see if categorial grammars can also achieve this challenge …