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AbstractMaterials science is about understanding the relationship between a material’s structure and its properties—in the sphere of mechanical behavior, this includes elastic modulus, yield strength, and other bulk properties. We show in this issue that, analogously, a material’s surface structure governs its surface properties—such as adhesion, friction, and surface stiffness. For bulk materials, microstructure is a critical component of structure; for surfaces, the structure is governed largely by surface topography. The articles in this issue cover the latest understanding of these structure–property connections for surfaces. This includes both the theoretical basis for how properties depend on topography, as well as the latest understanding of how surface topography emerges, how to measure and understand topography-dependent properties, and how to engineer surfaces to improve performance. The present article frames the importance of surface topography and its effect on properties; it also outlines some of the critical knowledge gaps that impede progress toward optimally performing surfaces. Graphical abstract