Mixed ionic-electronic conducting membranes have seen significant progress over the last 25 years as efficient ways to obtain oxygen separation from air and for their integration in chemical production systems where pure oxygen in small amounts is needed. Perovskite materials are the most employed materials for membrane preparation. However, they have poor phase stability and are prone to poisoning when subjected to CO2 and SO2, which limits their industrial application. To solve this, the so-called dual-phase membranes are attracting greater attention. In this review, recent advances on self-supported and supported oxygen membranes and factors that affect the oxygen permeation and membrane stability are presented. Possible ways for further improvements that can be pursued to increase the oxygen permeation rate are also indicated. Lastly, an overview of the most relevant examples of membrane reactors in which oxygen membranes have been integrated are provided.