The energy in flowing river streams, tidal currents or other artificial water channels is being considered as viable source of renewable power. Hydrokinetic conversion systems, albeit mostly at its early stage of development, may appear suitable in harnessing energy from such renewable resources. A number of resource quantization and demonstrations have been conducted throughout the world and it is believed that both in-land water resources and offshore ocean energy sector will benefit from this technology. In this paper, starting with a set of basic definitions pertaining to this technology, a review of the existing and upcoming conversion schemes, and their fields of applications are outlined. Based on a comprehensive survey of various hydrokinetic systems reported to date, general trends in system design, duct augmentation, and placement methods are deduced. A detailed assessment of various turbine systems (horizontal and vertical axis), along with their classification and qualitative comparison, is presented. In addition, the progression of technological advancements tracing several decades of R&D efforts are highlighted.