In alternative embodiments, the invention provides processes and methods for the recovery, removal or extracting of, and subsequent purification of uranium from a wet-process phosphoric acid using a continuous ion exchange processing approach, where the uranium is recovered from a phosphoric acid, or a phos-acid feedstock using either a dual or a single stage extraction methodology. In both cases an intermediate ammonium uranyl-tricarbonate solution is formed. In alternative embodiments, in the dual cycle approach, this solution is contacted in a second continuous ion exchange system with a strong anion exchange resin then subsequently recovered as an acidic uranyl solution that is further treated to produce an intermediate uranyl peroxide compound which is ultimately calcined to produce the final uranium oxide product. In alternative embodiments, in the single cycle case, the intermediate ammonium uranyl-tricarbonate solution is evaporated to decompose the ammonium carbonate and produce an intermediate uranium carbonate/oxide solid material. These solids are digested in an acid medium, and then processed in the same manner as the secondary regeneration solution from the dual cycle process to produce an intermediate uranyl peroxide that is calcined to produce a final uranium oxide product.