Scientists at the Idaho National Laboratory and Khlopin Radium Institute collaboratively developed and validated the concept of a Universal Extraction (UNEX) process for simultaneously removing the major radionuclides (Cs, Sr, actinides, and lanthanides) from acidic radioactive waste in a single solvent extraction process. The UNEX solvent incorporates three active extractants: chlorinated cobalt dicarbollide (CCD), polyethylene glycol (PEG), and diphenyl-NN-di-n-butylcarbamoylmethylphosphine oxide (CMPO), dissolved in a suitable organic diluent to simultaneously extract target radionuclides. The process chemistry is unique, but complicated, since the extractants operate synergistically to extract the major radionuclides. Furthermore, interactions with the diluent are quite important as the diluent strongly influences the extraction properties of the solvent system. We are studying the fundamental chemical phenomena responsible for the selective extraction of the different species to understand the underlying mechanisms and facilitate enhancements in process chemistry. Our efforts to date have relied on a combination of classical chemistry techniques, IR spectroscopy, and NMR spectroscopy to identify and explain the structures formed in the organic phase, elucidate the operative chemical mechanisms, and evaluate the diluent effects on extraction properties.