The genesis of this special issue was in a meeting that took place at Université Paris Diderot on December 15 and 16, 2016. Dale Miller, Professor at École polytechnique, had turned 60 a few days earlier. In a career spanning over three decades and in work conducted in collaboration with several students and colleagues, Dale had had a significant influence in an area that can be described as structural proof theory and its application to computation and reasoning. In recognition of this fact, several of his collaborators thought it appropriate to celebrate the occasion by organizing a symposium on topics broadly connected to his areas of interest and achievements. The meeting was a success in several senses: it was attended by over 35 people, there were 15 technical presentations describing new results, and, quite gratifyingly, we managed to spring the event as a complete surprise to Dale.