We report our recent efforts in developing the adaptive perfectly matched layer (PML) method solving the time-harmonic electromagnetic and acoustic scattering problems. The PML parameters such as the thickness of the layer and the absorbing medium property are determined through sharp a posteriori error estimates. Combined with the adaptive ﬁnite element method, the adaptive PML method provides a complete numerical strategy to solve the scattering problem in the framework of FEM which produces automatically a coarse mesh size away from the ﬁxed domain and thus makes the total computational costs insensitive to the choice of the thickness of the PML layer. Numerical experiments are
included to illustrate the competitive behavior of the proposed adaptive method.