Metamaterials have many special electromagnetic characteristics which are not available in natural materials, and it can control electromagnetic wave by properly designing. Researches on metamaterial asymmetric transmission devices are reviewed. The fundamental principle of asymmetric transmission of electromagnetic wave, research achievements of asymmetric transmission devices with linear polarized characteristics in GHz and THz bands and devices with circularly polarized wave are introduced respectively. Analysis shows that metamaterial asymmetric transmission devices are mainly focused on the microwave band, few research is carried out in terahertz band especially in the field of experimental verification. Finally, the development trend of metamaterial asymmetric transmission devices is discussed.