This special issue is devoted to complete and revised versions of papers presented at the Logique et Modèles du Calcul (Logic and Models of Computation) Conference held at CIRM in Marseilles in September 1996.

The conference was organized by Marie-Renée Donnadieu, and the members of the programme committee were Gérard Berry, Jean-Yves Girard, Max Kanovich, Jean-Louis Krivine, Yves Lafont and François Lamarche.

The scope of the conference was quite large, including, for instance, digital circuits, process calculi, abstract machines for lambda-calculus, computational interpretations of linear logic and logical aspects of proof search. Only the last three topics are represented in this special issue of Mathematical Structures in Computer Science, but we think that these papers are quite representative of the liveliness of research in this area on the borderline between mathematics and computing.

We wish to thank Giuseppe Longo, who kindly proposed publishing this issue. For editorial reasons, a few contributions could not be included – they should appear in later issues.