Metamaterials (MTMs) are artificial materials composed of subwavelength particles, which are engineered to achieve various electromagnetic (EM) responses. Since the first practical realization and experimental verification of MTMs by Pendry et al. in the late 1990s, great efforts have been made in theoretical study as well as practical utilizations. Among them, the effective medium theory provides a basis for the description as well as an accurate method for the design of MTMs, and leads to the development of many novel devices with interesting functionalities. With the employment of transformation and geometric optics, more high-performance engineering applications have been realized using MTMs. Recently, the concept of metasurfaces has been proposed, which further promotes the practical applications of advanced MTMs. Herein, the effective medium theory is first introduced. After that, typical devices and applications based on conventional bulk MTMs and newly-conceived metasurfaces are summarized to demonstrate the flexible capability of microwave MTMs in the manipulation of EM waves.Metamaterials are different from other periodic structures such as photonic crystals and frequency-selective surfaces (FSSs) because their unit cells are much smaller than the free-space wavelength. The subwavelength nature enables the metamaterials to Tianyi Chen received his B.Sc. degree from Southeast University, Nanjing, China, in 2013. He is currently working toward a Ph.D. degree in State Key Laboratory of Millimeter Waves at Southeast University. His research interests include metamaterials metasurfaces and antenna arrays. Wenxuan Tang received her B.Sc. and M.Sc. degrees from Southeast University, Nanjing, China, in Cheung-Kong Professor. His research interests include metamaterials, plasmonics in microwave, and computational electromagnetics.be treated as a homogenous effective medium and characterized by effective constitutive parameters. In early researches, closed formed expressions for the constitutive parameters were obtained in static and quasistatic limits, [86][87][88] which usually takes the form of Lorentz-Drude models. These results provided some intuition of the physical features but cannot quantitatively characterize metamaterials. In ref.[18], a numerical approach based on scattering (S) parameter retrieval was proposed to obtain the effective permittivity and permeability for periodic metamaterial structures. This method is accurate in the derivation of effective parameters. However it relies on full-wave simulation of metamaterial structures and hence is inefficient and difficult to be used in the design of large-volume metamaterials.In 2007, a general effective medium theory [17] was proposed by Liu et al., which sets up a relationship between particle responses and macroscopic behaviors of metamaterials. A closed form expression was provided to modify the Lorentz-Drude model, which takes the effects of spatial dispersion into account