The scope of computation has expanded dramatically beyond the rubric of discrete, deterministic sequential computation under which it has been studied for many decades. That focus, of course, led to a great deal of deep and beautiful theory, but our focus in this special issue of Mathematical Structures in Computer Science is on new directions that have emerged from the study of computational phenomena in other settings, and thus on a celebration of the diversity of ideas, methods, new applications and novel sources of inspiration that have marked the modern era. The papers in this issue come from sources extending far beyond the core of computer science, yet using many of the central ideas that have evolved within computer science and mathematics. The nexus of all this activity has been, on the one hand, the boundary between logic and computation, and, on the other hand, the natural sciences, particularly physics and biology. The papers in this collection are expanded versions of selected papers from the DCM 2010 workshop, which was held in Edinburgh in July 2010. The theme of the workshop was Causality, Computation and Physics.