Membrane technology has attracted great industrial interest in carbon capture and separation owing to the merits of energy-efficiency, environmental friendliness and low capital investment. Conventional polymeric membranes for CO₂ separation suffer from the trade-off between permeability and selectivity. Introducing porous fillers in polymers is one approach to enhance membrane separation performance. Metal-organic frameworks (MOFs), with ordered porous structure and diverse chemical functionalities, are promising fillers to prepare mixed matrix membranes (MMMs) for CO₂ separation. However, the main issue of MOF based MMMs in industry is their stability and processability. This review analyses recent work on stable and scalable MOF based MMMs for CO₂ separation. The typical stable MOFs, MOF-based MMMs and the scalable MOF synthesis are summarized. A large number of MOF-based MMM suffer from instability upon exposure to contaminants. For that reason, we also discuss the use of covalent organic frameworks (COFs) as an alternative to prepare MMMs for CO₂ separation, considering their excellent stability and good compatibility with polymers. Finally, a brief conclusion and current challenges on obtaining scalable and stable MMMs are outlined. This review may provide some guidance for designing high performance MMMs for industrial CO₂ capture and separation to help achieving carbon neutrality.