After a brief description of the PUREX process as a starting point, this paper aims to point out some of its most recent developments, always from the viewpoint of the chemistry involved in the solvent extraction methods. In addition to PUREX, other well-known technological approaches devoted to the reprocessing of irradiated uranium and thorium nuclear fuels and general radioactive wastes — TRUEX, DIAMEX, TRPO, DIDPA and UNEX — are also presented and discussed.