Abstract: Tangential point tracing grinding technology is a grinding technology, which keep the grinding wheel and machining surface tangency throughout grinding process. It is achieved by simultaneous moving the axis of workpiece spinning and that of grinding wheel feeding. This review starts with a summary of various motion models of tangential point tracing grinding technologies. Current research status of varying speed crank shaft spinning controlling methods, and origination and compensation of grinding error are summarized. And research status of machine tool design, development of electrical system and control system, programming interpolation, artificial intelligence deciding processing parameters and automatic positioning are also discussed. It is pointed out that the constant equivalent grinding thickness method equals the constant speed grinding method, in condition that the spinning speed of grinding wheel is far larger than that of crank shaft. And the so called error caused by radius variation of grinding wheel is a residue error of primitive radius compensation.