CO2 resistance is an enabling property for the wide-scale implementation of oxygen-selective mixed ionic-electronic conducting (MIEC) membranes in clean energy technologies, i.e., oxyfuel combustion, clean coal energy delivery, and catalytic membrane reactors for greener chemical synthesis. The significant rise in the number of studies over the past decade and the major progress in CO2-resistant MIEC materials warrant systematic guidelines on this topic. To this end, this review features the pertaining aspects in addition to the recent status and advances of the two most promising membrane materials, perovskite and fluorite-based dual-phase materials. We explain how to quantify and design CO2 resistant membranes using the Lewis acid-base reaction concept and thermodynamics perspective and highlight the relevant characterization techniques. For perovskite materials, a trade-off generally exists between CO2 resistance and O2 permeability. Fluorite materials, despite their inherent CO2 resistance, typically have low O2 permeability but this can be improved via different approaches including thin film technology and the recently developed minimum internal electronic short-circuit second phase and external electronic short-circuit decoration. We then elaborate the two main future directions that are centralized around the development of new oxide compositions capable of featuring simultaneously high CO2 resistance and O2 permeability and the exploitation of phase reactions to create a new conductive phase along the grain boundaries of dual-phase materials. The final part of the review discusses various complimentary characterization techniques and the relevant studies that can provide insights into the degradation mechanism of oxide-based materials upon exposure to CO2.