Terahertz (THz) science and technology have been developed rapidly over the past decade due to its superiority in security, communication, imaging, and spectroscopy. In order to manipulate THz waves efficiently, many THz functional materials and devices have been proposed. Metasurfaces with subwavelength elements arranged in a periodic or quasi-periodic manner have been widely investigated. The amplitude, phase and polarization state can be controlled flexibly by designing the geometry. In this paper, several typical THz electromagnetic functional materials will be introduced, magnetic-optical semiconductors, nanoparticle liquid crystal, 3D graphene foam, carbon nanotubes, etc. These electromagnetic functional materials show unique functions for THz active modulation, polarization conversion, one-way transmission, and perfect absorption. Combined with these new materials, we designed and fabricated a series of THz metasurface device to enhance or expand the functions of these functional materials. Meanwhile, the introduction of functional materials brings THz metasurfaces into the active properties. The combination of these artificial micro-structures and electromagnetic functional materials bring new development for active or multifunctional THz devices.