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We describe the evolution of coastal HF radar observations of tsunamis, first proposed in 1979 and developed after the 2004 Indonesia and 2011 Japan tsunamis to allow routine monitoring to detect an approaching tsunami. Oceanographic tsunami theory is summarized, both for the fundamental equations of motion and in the ray optics and Green's Law approximations; the latter can be applied when water depths are slowly varying. Observations of the current velocities caused by the 2011 Japan tsunamidoi:10.5772/63960 fatcat:fatmx2h5brapbmwjauvhaw3zv4