Separation of liquid–liquid emulsions is a challenging problem that has gained importance with the development of unconventional oil resources. Large volumes of water contaminated by emulsified oil need to be treated for safe disposal or efficient reuse. Among technologies capable of removing oil dispersed into smaller size droplets (<15 µm), membrane processes occupy a unique niche where the required separation performance and throughput can be achieved at a relatively modest cost. As with most membrane-based processes, separation of emulsified oil entails membrane fouling that requires regular maintenance and imposes additional operational costs. Emulsions present unique challenges as their fouling behavior is affected by droplets’ deformability, coalescence both in the bulk and on the membrane surface, membrane wetting by droplets and films, pore blockage and intrusion by oil. The purpose of this paper is to overview the literature on the separation of oil–water emulsions by pressure-driven membrane processes with an emphasis on how properties of emulsions and membranes affect separation performance. A particular focus is on membrane fouling by oil including physicochemical bases, detection, diagnosis, and visualization. The review spans studies with both industrial oily wastewater and synthetic model emulsions of various types of oil. The discussion of membrane materials is limited to surface modifications that render more fouling-resistant membranes.