Skyrmions in magnetic materials offer attractive perspectives for future spintronic applications since they are topologically stabilized spin structures on the nanometre scale, which can be manipulated with electric current densities that are by orders of magnitude lower than those required for moving domain walls. So far, they were restricted to bulk magnets with a particular chiral crystal symmetry greatly limiting the number of available systems and the adjustability of their properties. Recently, it has been experimentally discovered that magnetic skyrmion phases can also occur in ultra-thin transition metal films at surfaces. Here we present an understanding of skyrmions in such systems based on first-principles electronic structure theory. We demonstrate that the properties of magnetic skyrmions at transition metal interfaces such as their diameter and their stability can be tuned by the structure and composition of the interface and that a description beyond a micromagnetic model is required in such systems.