Single-atom catalysts are a frontline approach in catalysis research. In these materials, isolated atoms of a metal are dispersed and stabilized on a host material. If the substrates are metals, we identify these materials as single-atom alloys (SAAs). Thus, SAAs are metallic systems in which one single atom of a given chemical element is embedded in a monometallic host surface of a second element. We denote these systems hereafter as SA@host. SAAs can display unique electronic properties compared to monometallic systems or stoichiometric alloys. These properties can be exploited to design new catalysts. Particularly, the adsorption strength of reactive species with the materials surface can be modulated by the choice of the SA and host elements, and by the geometry of the adsorption sites containing the SA. Several methods for the synthesis of SAAs and applications in catalysis have been reported. SAAs are typically designed by embedding a highly active SA element on the surface of a less active host element. This is done to enable the desired reaction while avoiding undesirable side (competing) reactions that would occur in systems of pure, highly active metals. Thus, the selectivity can be improved. Additionally, it has been shown that SAAs can display enhanced stability during time on stream (operation). However, due to the practically infinite compositional and structural space, designing SAAs for catalysis is a formidable challenge.