The highly efficient energy conversion of the polymer-electrolyte-membrane fuel cell (PEMFC) is extremely limited by the sluggish oxygen reduction reaction (ORR) kinetics and poor electrochemical stability of catalysts. Hitherto, to replace costly Pt-based catalysts, non-noble-metal ORR catalysts are developed, among which transition metal-heteroatoms-carbon (TM-H-C) materials present great potential for industrial applications due to their outstanding catalytic activity and low expense. However, their poor stability during testing in a two-electrode system and their high complexity have become a big barrier for commercial applications. Thus, herein, to simplify the research, the typical Fe-N-C material with the relatively simple constitution and structure, is selected as a model catalyst for TM-H-C to explore and improve the stability of such a kind of catalysts. Then, different types of active sites (centers) and coordination in Fe-N-C are systematically summarized and discussed, and the possible attenuation mechanism and strategies are analyzed. Finally, some challenges faced by such catalysts and their prospects are proposed to shed some light on the future development trend of TM-H-C materials for advanced ORR catalysis.