This special issue of Mathematical Structures in Computer Science is devoted to recent work in subtyping. When subtyping was first proposed, it presented a new vehicle for understanding programming languages, together with challenging theoretical issues. The papers in this special issue include a new approach to the decidability of subtyping, a metatheoretic investigation of transitivity of coercive subtyping for parametrised dependent types, and applications of subtyping to the classic programming language concerns of flow analysis and typing for distributed systems. We believe that the scope of the papers demonstrates convincingly that the theory and practice of subtyping continue to be extended in novel and interesting ways.