Methods of making glucose and/or furfural from biomass require one or more supercritical fluids that may be used to process biomass, cellulose from the biomass, and/or xylose from the biomass. Examples of supercritical fluids for use in processing biomass include ethanol, water, and carbon dioxide at a temperature and pressure above the critical points for ethanol and carbon dioxide but at a temperature and/or pressure below that of the critical point for water. A supercritical fluid containing carbon dioxide and water may be used to convert cellulose to glucose or convert xylose to furfural. The fluid has a temperature and pressure above the critical point of carbon dioxide, but at least one of the temperature and pressure is below the critical point for water.