The modified competitive preferential solvation (COPS) theory together with the concepts of aggregation stages and amphoteric properties of extractants are introduced to explain the mechanisms of solvent extraction of acids by different basic or mixed (acid-base, base-base) extractants. According to the modified COPS theory, the molecules of a solvent mixture (extractant, diluent, adduct) compete for acid to the extent of their affinity to associate and be concentrated. The acid is partitioned among the solvent components. As a consequence, an actual value of a given property in mixed solvents can be calculated from its values measured in pure solvent components. The theory establishes the connection between complexation and solvation. Four possible stages of extraction behavior and interacting mechanisms that depend on acid-solvent affinity constant ratios and acid concentration are discussed. At low or very low acid concentrations in the organic phase, the acid-amine complex, surrounded by its solvation shell, forms a geometric structure that is denoted as a nucleus aggregate. When the acid concentration is increased, the nucleus aggregates interact and form linear or ringed (cyclic) aggregates. At high acid concentration the linear (planar) aggregates eventually undergo a structural reorganization to form micelle-like or cross-linked cluster-like association structures (as a rule, forming a so-called third phase). Extractants are considered amphoteric and may perform as acids (electron acceptors) or bases (electron donors), depending on the structure of their functional groups and composition of the organic phase and on the structure of the solutes and composition of the aqueous phase. A mathematical description for result quantification is also introduced. On the basis of the presented theory, analysis of different extraction systems are discussed and some predictions are made.