Single-molecule magnets (SMMs) offer stable quantum objects capable of exhibiting diverse magnetic states on the nanoscale, making them promising candidates for storing and processing quantized information at the molecular level. While substantial progress has been made in studying isolated SMMs over the past three decades, with particular emphasis on complexes containing rare-earth ions and endohedral metallofullerenes, the design of stable SMMs on solid surfaces remains a significant challenge for their practical application in electronic devices. In this Perspective, we reviewed recent advancements of SMMs on suitable solid surfaces that can retain and even enhance their magnetic properties. We discuss promising SMMs and the relevant physical parameters that contribute to their magnetic properties. By employing first-principles density functional theory methodologies, we primarily explore the intricate interactions between SMMs and surfaces, emphasizing the need for further theoretical investigations to bridge the gap and enable the design of functional SMMs on surfaces.