Biorefineries, which process biomass feedstocks into valuable (bio)products, aim to replace fossil fuel-based refineries to produce energy and chemicals, reducing environmental and health hazards, including climate change, and supporting a sustainable economy. In particular, lignocellulose-based biorefineries, utilizing the most abundant renewable feedstock on Earth, have significant potential to supply sustainable energy, chemicals and materials. Ionic liquids (ILs, organic salts with low melting temperatures) and deep eutectic solvents (DESs, mixtures with eutectic points lower than the ideal mixture) are capable of dissolving some of the key lignocellulose polymers, and even the whole biomass. Furthermore, they have intrinsic advantages over molecular solvents, including safer usage profiles and high tunability, which allow tailored physicochemical properties. Such properties provide unique opportunities for the development of new processes that could unlock the full potential of future biorefineries. Here, we review the current state of lignocellulosic biomass processing with ILs and DESs, with a specific focus on the pretreatment chemistry, process flow and products from each component; followed by discussions on sustainability assessments and technological challenges. We aim to inform the research community about the opportunities, challenges and perspectives in developing truly sustainable lignocellulose-based biorefineries.