This book presents transmission properties in one- and two-dimensional plasmonic metamaterials with periodically and randomly structured arrays of various shaped perforated-apertures on metallic surfaces in the terahertz region. At a specific frequency at which the plasmonic metamaterials are perfectly transparent, the metal materials become essentially invisible. In the case of one-dimensional arrays of slits, Fabry-Perot like shape resonance enhances transmission of nearby horizontal surface resonance by the periodicity. Whereas in the case of two-dimensional arrays of various shaped holes, the shape resonance supported by guided-mode resonance, generally cutoff frequency, enhances transmission to be essentially unity near specific resonance frequencies. These understanding for the perfect transmission in the plasmonic metamaterials can contribute to the development of sensitive imaging systems, waveguides, and terahertz and infrared transmission filters.