Methods are disclosed herein to extract, concentrate and fractionate proteins and protein-associated complexes with other polymers from soybeans, peanuts, rape, canola, cottonseeds, peas, wheat and other plant materials, based on a principle of cryoprecipitation. The disclosed methods involve no or minimal uses of chemicals, and generate a minimal volume of waste streams. The resulting protein concentrates or isolates have excellent functionality, superior nutritional quality, attractive appearance and mild taste. Based on the sample principle of cryoprecipitation, methods also are also disclosed to extract and concentrate chemical components from living tissues, especially some nutraceutical or phytochemical components from plant materials.