A method for extracting rare earth elements from aqueous solution, comprising: (i) acidifying an aqueous solution containing said rare earth elements with an inorganic acid to result in an acidified aqueous solution containing said rare earth elements and containing the inorganic acid in a concentration of 1-12 M, wherein said rare earth elements are selected from lanthanides, actinides, or combination thereof; and (ii) contacting the acidified aqueous solution with an aqueous-insoluble hydrophobic solution comprising a rare earth extractant compound dissolved in an aqueous-insoluble hydrophobic solvent to result in extraction of one or more of the rare earth elements into the aqueous-insoluble hydrophobic solution by binding of the rare earth extractant compound to the one or more rare earth elements, wherein the rare earth extractant compound has the structure of Formula (1) provided that at least one of the conditions (a)-(d) applies.