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[Display omitted] • M-N-C/MoS 2 heterostructures exhibit good structural stability, excellent electrical conductivity, and improved stiffness. • The anchored Ir-N-C, Rh-N-C, and Co-N-C are identified as eligible bifunctional ORR/OER electrocatalysts. • The optimal binding strength with the oxygenated intermediates endow anchored M-N-C good catalytic performance. The development of highly-efficient bifunctional oxygen electrocatalysts is essential to the large-scale commercialization of energy-related conversion and storage technologies. In this work, using first-principle computations, we systematically investigated the catalytic activities of a variety of metal-N-C/MoS 2 heterostructures (M-N-C/MoS 2 , M = Cr, Mn, Fe, Co, Ni, Cu, Zn, Ru, Rh, Pd, Ag, Os, Ir, and Pt) towards the oxygen reduction/evolution reactions (ORR/OER). Our result revealed that these M-N-C/MoS 2 heterostructures exhibit good structural stability, excellent electrical conductivity, and improved stiffness. Furthermore, the anchored Ir-N-C was identified as the best bifunctional ORR/OER electrocatalyst due to its lowest overpotentials (0.28/0.38 V) among all candidates, which were well rationalized by its optimal binding strength with the oxygenated intermediates. Thus, by combining M-N-C and MoS 2 monolayer, the highly-efficient bifunctional ORR/OER electrocatalysts can be achieved, which offers a new strategy to further explore heterostructures-based materials for other electrochemical processes. [ABSTRACT FROM AUTHOR]