Membrane-based separations have garnered considerable attention owing to their high energy efficiency, low capital cost, small carbon footprint, and continuous operation mode. As a class of highly porous crystalline materials with well-defined pore systems and rich chemical functionalities, metal–organic frameworks (MOFs) have demonstrated great potential as promising membrane materials over the past few years. Different types of MOF-based membranes, including polycrystalline membranes, mixed matrix membranes (MMMs), and nanosheet-based membranes, have been developed for diversified applications with remarkable separation performances. In this comprehensive review, we first discuss the general classification of membranes and outline the historical development of MOF-based membranes. Subsequently, particular attention is devoted to design strategies for MOF-based membranes, along with detailed discussions on the latest advances on these membranes for various gas and liquid separation processes. Finally, challenges and future opportunities for the industrial implementation of these membranes are identified and outlined with the intent of providing insightful guidance on the design and fabrication of high-performance membranes in the future.