Oxygen transport membranes are considered important devices in future separation processes associated with energy, environmental, and biomedicine. Innovative core-shell structured diffusion-bubbling membranes (DBM) with high oxygen permeability and theoretically infinite selectivity are promising candidates for efficient oxygen separation from air. The combined diffusion-bubbling oxygen mass transport allows a substantial degree of flexibility in membrane material design. Compared to conventional mixed-conducting ceramic membranes, DBM have several advantages (e.g. highly mobile bubbles as oxygen carriers, the low energy barrier for oxygen ion migration in the liquid phase, flexibility and tightness of the selective shell, simplicity and ease of the membrane material fabrication, and low cost) and therefore could be used successfully for oxygen separation. This perspective briefly reviews the current state of research into a new type of oxygen permeable membranes, the core-shell structured DBM, and outlines directions for future research.