After 70 years, modern pressure‐driven polymer membrane processes with liquids are mature and accepted in many industries due to their good performance, ease of scale‐up, low energy consumption, modular compact construction, and low operating costs compared with thermal systems. Successful isothermal operation of synthetic membranes with liquids requires consideration of three critical aspects or “legs” in order of relevance: selectivity, capacity (i.e. permeation flow rate per unit area) and transport of mass and momentum comprising concentration polarization (CP) and fouling (F). Major challenges remain with respect to increasing selectivity and controlling mass transport in, to and away from membranes. Thus, prediction and control of membrane morphology and a deep understanding of the mechanism of dissolved and suspended solute transport near and in the membrane (i.e. diffusional and convective mass transport) is essential. Here, we focus on materials development to address the relatively poor selectivity of liquid membrane filtration with polymers and discuss the critical aspects of transport limitations. Machine learning could help optimize membrane structure design and transport conditions for improved membrane filtration performance.