A synergistic extraction mixture containing chlorinated cobalt dicarbollide (CCD), polyethylene glycol (PEG), and diphenyl-N,N-dibutylcarbamoyl phosphine oxide (CMPO) in a suitable polar diluent is being developed for the simultaneous recovery of Cs, Sr, and the actinides from highly acidic radioactive wastes. Development of this UNEX process was by a successful collaboration between scientists from the Idaho National Engineering and Environmental Laboratory (INEEL) and the Khlopin Radium Institute (KRI) in St. Petersburg, Russia. Development efforts focused on the treatment of radioactive waste currently stored at the INEEL. The development of the UNEX process has and continues to be an evolutionary process. Numerous countercurrent flowsheet demonstrations have been conducted to date, including two tests with several liters of actual radioactive tank waste, one test with dissolved radioactive calcine, and several tests with surrogate INEEL tank and dissolved calcine wastes. All countercurrent flowsheet tests have been performed in banks of centrifugal contactors. Removal efficiencies of 99.95% for Cs-137, 99.995% for Sr-90, and 99.96% for total alpha (predominately Am-241, Pu-238, and Pu-239) were observed in countercurrent tests with samples of actual INEEL tank waste. The evolutionary concepts included in the development of the UNEX process are discussed, including development of the current diluent, phenyltrifluoromethyl sulfone, to replace nitroaromatic diluents used in earlier studies. Results from the most recent countercurrent flowsheet testing with 1.2 L of actual dissolved INEEL calcine are also presented, which represents the current state of UNEX development. Finally, future research directions in the development and understanding of the UNEX process are discussed.