In the quest for a sustainable bio-based economy, biorefineries play a central role as they involve the sustainable processing of biomass into marketable products and energy. This paper aims to provide a perspective on applications of separations that can make a great difference in biorefineries, by significantly reducing the costs and thus making the processes competitive without subsidies. A parallel is drawn between bio-refinery and petro-refinery, to highlight the specific separation challenges encountered in biorefineries and point out the impact of separations on the total costs. Existing and foreseen separations in biorefineries are reviewed, and the upcoming challenges in the bio-domain (additional to current fossil) are identified. Relevant industrial examples are provided to illustrate the tremendous eco-efficiency benefits of well-designed separation processes based on process intensification principles (e.g. reactive separations, dividing-wall column, affinity and trigger-enhanced separations). These examples also illustrate the low sustainability of several bio-separations currently practiced, in terms of high relative energy requirements, large amounts of gypsum co-production and/or excess use of caustic.