Abstract: The invention herein is an efficient, flexible biomass fractionation process comprising digesting a lignocellulosic-biomass material at about 120-220° C. and a pH of less than about 4, in an aqueous mixture containing an effective concentration of at least one solvent for lignin, and separating to recover a solid phase that contains a large fraction of the cellulose originally in the starting lignocellulosic material and a liquid phase that contains most of the lignin and hemicellulose originally in the starting lignocellulosic biomass. The process can produce a solid phase that contains at least 75% cellulose and less than 10% lignin. The cellulose-rich solid product can be converted very efficiently to glucose. The solid product can also be used in commercial pulp applications, such as papermaking or fluff pulp. Hemicellulose sugars and lignin can be used directly or converted to other products.