This special issue of Mathematical Structures in Computer Science is dedicated to the memory of Barry Cooper (October 9, 1943–October 26, 2015). Barry's life in research had a huge impact on the development of the world of computability. Aside from his enormous achievements in classical computability theory, he contributed immensely to the promotion of interdisciplinary developments related to computability, in particular, by founding the Association for Computability in Europe (CiE) and its annual, highly successful conference series.