This chapter covers the process of oxygen-reduction reaction (ORR) for fuel-cell systems of nonprecious electrocatalyst centers explored since the 1960s, showing the progress achieved with regard to their catalytic activity and stability. The catalytic centers investigated so far are transition metal chalcogenides and metal-macrocycles; in particular, the chalcogenides and the macrocycles containing cobalt or iron metals. The chapter also displays the progress made via theoretical studies on non-noble metal chalcogenides made in understanding of the ORR mechanism and factors that affect the ORR activity and stability.Peer reviewed: YesNRC publication: Ye