Single-atom catalysis is a powerful and attractive technique with exceptional performance, drastic cost reduction and notable catalytic activity and selectivity. In single-atom catalysis, supported single-atom catalysts contain isolated individual atoms dispersed on, and/or coordinated with, surface atoms of appropriate supports, which not only maximize the atomic efficiency of metals, but also provide an alternative strategy to tune the activity and selectivity of catalytic reactions. This review will highlight the attributes of single-atom catalysis and summarize the most recent advancements in single-atom catalysts with a focus on the design of highly active and stable single atoms. In addition, new research directions and future trends will also be discussed.