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We give a short personally-biased review on the recent progress in our understanding of gravitational radiation reaction acting on a point particle orbiting a black hole. The main motivation of this study is to obtain sufficiently precise gravitational waveforms from inspiraling binary compact stars with a large mass ratio. for this purpose, various new concepts and techniques have been developed to compute the orbital evolution taking into account the gravitational self-force. Combining these ideas with a few supplementary new ideas, we try to outline a path to our goal here.
Takahiro Tanaka (Sun,) studied this question.