Terahertz science and technology promise many cutting-edge applications. Terahertz surface plasmonic waves that propagate at metal–dielectric interfaces deliver a potentially effective way to realize integrated terahertz devices and systems. Previous concerns regarding terahertz surface plasmonic waves have been based on their highly delocalized feature. However, recent advances in plasmonics indicate that the confinement of terahertz surface plasmonic waves, as well as their propagating behaviors, can be engineered by designing the surface environments, shapes, structures, materials, etc., enabling a unique and fascinating regime of plasmonic waves. Together with the essential spectral property of terahertz radiation, as well as the increasingly developed materials, microfabrication, and time-domain spectroscopy technologies, devices and systems based on terahertz surface plasmonic waves may pave the way toward highly integrated platforms for multifunctional operation, implementation, and processing of terahertz waves in both fundamental science and practical applications. We present a review on terahertz surface plasmonic waves on various types of supports in a sequence of properties, excitation and detection, and applications. The current research trend and outlook of possible research directions for terahertz surface plasmonic waves are also outlined.