Perfectly transparent metamaterial structures of arbitrary shapes, constructed from coordinate stretching and contractions, are presented. Coordinate stretching has been used for 2 decades in perfectly matched layers (PMLs) to electromagnetically simulate infinite domains in numerical techniques, but this concept is applied here for the first time to realize a physical transmission medium. The transparent medium does not scatter electromagnetic waves, i.e. it is reflection-less for all incidence angles and all excitation frequencies. It may be implemented in the form of metasurfaces and will clearly find a myriad of applications if it can be efficiently manufactured.