Nowadays, an increasing emission of chemically resistant perfluorinated compounds (PFCs) to the natural environment, together with a global presence of those anthropogenic pollutants in both natural and treated waters and in both human and animal organisms, poses a great environmental challenge. A limited efficiency of their removal by commonly employed technologies prompts a search for more efficient and more cost-effective methods. Recent decades brought in water management an intense progress in Advance Oxidation Processes, based on decomposition of pollutants by free radicals, which can be produced in different ways. This review presents the recent advances in those methods for decomposition of the most commonly occurring PFCs in the natural environment - perfluorooctanoic acid (PFOA) and perfluorooctane sulfonic acid (PFOS). For this purpose, there have been developed particular methods based on an oxidation and reduction of target pollutants, generally abbreviated as AO/RPs. The review, which was based on 180 cited references, includes photolytic and photocatalytic methods, electrochemical processes as well as sonolytic and radiolytic methods with the use of ionizing radiation, wet chemnical oxidation methods, ozonation and Fenton processes. Attempts on comparison of the developed methods, their applications to real samples and molecular mechanisms of occurring transformations are provided.