Methods are provided for separation of substances using non-crystalline, amorphous inorganic oxides having mesoporosity or combined meso- and microporosity. The amorphous inorganic oxide may have a separating agent, such as a chemical functional group, bonded or attached to the surfaces within the pores. The amorphous inorganic material is exposed to a fluid containing two or more materials to be separated. At least one material contained in the fluid is preferentially retained by the amorphous inorganic oxide either on the surface of the inorganic oxide within the pores or by interaction with a separating agent group attached to the pore surfaces.