As chemical reactions and charge-transfer simultaneously occur on the catalyst surface during electrocatalysis, numerous studies have been carried out to attain an in-depth understanding on the correlation among the surface structure and composition, the electrical transport, and the overall catalytic activity. Compared with other catalysis reactions, a relatively larger activation barrier for oxygen evolution/reduction reactions (OER/ORR), where multiple electron transfers are involved, is noted. Many works over the past decade thus have been focused on the atomic-scale control of the surface structure and the precise identification of surface composition change in catalyst materials to achieve better conversion efficiency. In particular, recent advances in various analytical tools have enabled noteworthy findings of unexpected catalytic features at atomic resolution, providing significant insights toward reducing the activation barriers and subsequently improving the catalytic performance. In addition to summarizing important surface issues, including lattice defects, related to the OER and ORR in this Review, we present the current status and discuss future perspectives of oxide- and alloy-based catalysts in terms of atomic-scale observation and manipulation.