Metamaterials have been developed as a new class of artificial effective media realizing many exotic phenomena and unique properties not normally found in nature. Metamaterials enable functionality through structure design, facilitating applications by addressing the severe material issues in the terahertz frequency range. Consequently, prototype functional terahertz devices have been demonstrated, including filters, antireflection coatings, perfect absorbers, polarization converters, and arbitrary wavefront shaping devices. Further integration of functional materials into metamaterial structures have enabled actively and dynamically switchable and frequency tunable terahertz metamaterials through the application of external stimuli. The enhanced light-matter interactions in active terahertz metamaterials may result in unprecedented control and manipulation of terahertz radiation, forming the foundation of many terahertz applications. In this paper, we review the progress during the past few years in this rapidly growing research field. We particularly focus on the design principles and realization of functionalities using single-layer and fewlayer terahertz planar metamaterials, and active terahertz metamaterials through the integration of semiconductors to achieve switchable and frequency-tunable response.