Abstract
The logical approach to categorial grammars renews ideas that go back to the fifties (and even to the thirties) and recent research connects those linguistic formalisms to type systems of the sort familiar in computer science. This new trend in computational linguistics is nevertheless tightly related to more common formalisms for natural language processing, like tree adjoining grammars, dependency grammars, and certain phrase-structure grammars. What is the motivation of such an approach ? What are its successes ? What are its objectives ? This survey tries to answer these questions, stressing the important role of logic in recent developments and the tight connection with semantics. Basic results are precisely covered while more recent research and insights are only informally presented.