With the rapid economic growth and the deepening awareness of sustainable development, the demand for green and efficient energy storage equipment increases. As a promising energy storage and conversion device, zinc-air batteries (ZABs) have the advantages of high theoretical specific energy density, low cost, and environmental friendliness. Nevertheless, the efficiency of ZABs is closely related to the electrocatalytic capacity of the air electrode due to its sluggish kinetics for oxygen reduction and evolution reaction (ORR/OER). Therefore, it is necessary to develop efficient catalysts to promote the reaction rate. Recently, cobalt-based materials have become a research hotspot for oxygen electrocatalysts owing to their rich natural content, high catalytic activity, and stability. In this review, the mechanisms of the OER/ORR reaction process, the catalyst’s performance characterization, and the various combination methods with the current collector are systematically introduced and analyzed. Further, a broad overview of cobalt-based materials used as electrocatalysts for ZABs is presented, including cobalt-based perovskite, cobalt-nitrogen-carbon (Co−N−C) materials, cobalt oxides, cobalt-containing composite oxides, and cobalt sulfides/phosphides. Finally, various strategies for developing efficient electrocatalysts for ZABs are summarized, highlighting the challenges and future perspectives in designing novel catalysts.