The DPW method determines classes of surfaces with special features (minimal surfaces, surfaces of constant mean or Gaussian curvature and Willmore surfaces), by means of loop groups. The harmonicity of special maps associated to these surfaces is characterized in terms of meromorphic potentials of a certain shape. The link between these concepts is performed using the Birkhoff and Iwasawa decomposition for loop groups. The paper presents the main features of the method and describes explicitly these decompositions in an extended framework which includes the non-semisimple case.