Introduction 9870 1.1. Background 9870 1.2. Oxygen Catalysts 9871 1.3. Nonstoichiometric Oxides 9872 2. ABO 3-δ Perovskite-Type Catalysts 9873 2.1. General Introduction 9873 2.2. Ba 0.5 Sr 0.5 Co 0.8 Fe 0.2 O 3−δ Oxygen Catalysts 9873 2.3. Effects of Cations 9876 2.3.1. Effects of A-Site Cations 9876 2.3.2. Effects of B-Site Cations 9877 2.3.3. Effects of A′-Site Cations 9878 2.3.4. Effects of B′-Site Cations 9879 2.4. Extrinsic Strategies for Enhancing Performance and Stability 9880 2.4.1. Controlling Phase Structure and Surface Activities 9880 2.4.2. Nanostructured Materials 9881 2.4.3. Crystallographic Orientations 9884 2.4.4. Amorphous Phases 9886 2.4.5. Composites 9886 2.5. Summary 9886 3. Layered-Perovskite-Type Catalysts 9887 3.1. Ruddlesden−Popper Phases 9887 3.2. Double Perovskites 9887 3.3. Summary 9889 4. Pyrochlore-Type Catalysts 9890 4.1. Structure and Properties 9890 4.2. Summary 9891 5. Other Typical Nonstoichiometric Oxides 9891 5.1. MnO x Oxygen Catalysts 9891 5.2. Ceria-Related Oxygen Catalysts 9892 5.3. NiO x -Based Oxygen Catalysts 9893 5.4. Delithiated LiCoO 2 −Related Oxygen Catalysts 9894 5.5. Summary 9894 6. Benchmarking Oxygen Catalysts 9894 6.1. Overview of the State-of-the-Art Oxygen Catalysts 9894 6.2. ORR/OER Bifunctional Oxygen Catalysts 9895 7. Design Principles 9897 7.1. Descriptors from Molecular Orbital Theory 9897 7.2. Descriptors from DFT Calculations 9899 8. Mechanistic Understanding 9900 9. Summaries and Research Directions 9904 9.1. Perovskite-Type Oxygen Catalysts 9904 9.2. Pyrochlore-Type Oxygen Catalysts 9904 9.3. MnO x , CeO x , and NiO x Related Oxygen Catalysts 9904 9.4. Catalyst Support 9904 9.5. Electrode Architectures 9905 9.6. Solid Electrolytes/Separators/Protectors 9905 9.7. System 9905 9.8. Advanced Characterizations 9905 9.9. Transferring Current Materials 9905 9.10.

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