Aqueous organic redox-flow batteries (AORFBs) are an emerging technological solution in the field of grid-scale energy storage, owing to their long lifetime, safety, chemical flexibility, potentially low costs and environmental friendliness. Membranes are a crucial component of the battery as they affect the ohmic resistance and the power density of the cells, as well as the depth-of-discharge and the lifetime and thus, crucially affect the levelised cost of storage of the battery. Herein, we provide a critical discussion of the state-of-the-art literature on membranes for AORFBs, including a summary on the theories used to model the transport of ions and active species through the membrane, as well as a compilation of experimental correlations between various membrane properties and cell performance. Adequate strategies to further improve the performance and lower the cost of AORFBs by employing and designing appropriate membranes are highlighted. Finally, the remaining challenges are summarised and perspectives on future research directions for developing appropriate and low-cost membranes for AORFBs are outlined.