The review substantiates the desirability of developing spent nuclear fuel reprocessing technologies alternative to the Purex process. The practical use of radiochemical technologies based on alkaline and carbonate media, such as extraction of radiocesium from alkaline high-level waste and CARBEX process, is considered. Extraction of actinides with aliphatic amines, β-diketones, phenol derivatives (alkylpyrocatechols, aminomethylphenols, alkylphenol oligomers, calixarenes), and carboxylic acids, as well as extraction in two-phase aqueous systems based on water-soluble polymers, is discussed. The extraction of technetium is considered separately.