The fabrication and investigation of single and multilayered structures have become an essential issue in the past decades since these structures directly define valuable properties and efficiency of widely used terahertz (THz) emitters and detectors. Since the development of molecular-beam epitaxy, as well as other crystal growth techniques, a variety of structural designs has appeared and has been proposed. Since that, an enormous progress has been achieved beginning from the pioneering work on photoconductivity in silicon toward different multilayered heterostructures. The last are now commonly utilized as base components in photoconductive THz emitters/detectors, quantum-cascade lasers for pulsed and continuous-wave THz spectroscopic and imaging systems providing critical fundamental and practical applications at the forefront of scientific knowledge (sensors, flexible electronics, security systems, biomedicine, and others). This review summarizes the developments in different approaches and crystal growth techniques, emphasizing the importance of using single and multilayered arsenides-and related III-V materials-based (phosphides, antimonides, bismuthides) structures to accomplish the needs of modern and existing instruments of THz science and technology.