K-stability of Fano manifold is recently proved to be equivalent to the existence of Einstein-Kahler metric. After brifely explaining the recent developement of the differential geometric background by Chen-Donaldson-Sun and Tian, I would like to revisit my algebro-geometric works done a few years ago about the following question: "When a Fano manifold really is K-stable?". In general, this remains as a hard algebro-geometric but important question.