Abstract: Terahertz metamaterials comprise a periodic array of resonator elements disposed on a dielectric substrate or thin membrane, wherein the resonator elements have a structure that provides a tunable magnetic permeability or a tunable electric permittivity for incident electromagnetic radiation at a frequency greater than about 100 GHz and the periodic array has a lattice constant that is smaller than the wavelength of the incident electromagnetic radiation. Microfabricated metamaterials exhibit lower losses and can be assembled into three-dimensional structures that enable full coupling of incident electromagnetic terahertz radiation in two or three orthogonal directions. Furthermore, polarization sensitive and insensitive metamaterials at terahertz frequencies can enable new devices and applications.