High‐performance and inexpensive platinum‐group‐metal (PGM)‐free catalysts for the oxygen reduction reaction (ORR) in challenging acidic media are crucial for proton‐exchange‐membrane fuel cells (PEMFCs). Catalysts based on Fe and N codoped carbon (Fe–N–C) have demonstrated promising activity and stability. However, a serious concern is the Fenton reactions between Fe2+ and H2O2 generating active free radicals, which likely cause degradation of the catalysts, organic ionomers within electrodes, and polymer membranes used in PEMFCs. Alternatively, Co–N–C catalysts with mitigated Fenton reactions have been explored as a promising replacement for Fe and PGM catalysts. Therefore, herein, the focus is on Co–N–C catalysts for the ORR relevant to PEMFC applications. Catalyst synthesis, structure/morphology, activity and stability improvement, and reaction mechanisms are discussed in detail. Combining experimental and theoretical understanding, the aim is to elucidate the structure–property correlations and provide guidance for rational design of advanced Co catalysts with a special emphasis on atomically dispersed single‐metal‐site catalysts. In the meantime, to reduce H2O2 generation during the ORR on the Co catalysts, potential strategies are outlined to minimize the detrimental effect on fuel cell durability.