We explain a recent work with Huang where we combine various results in complex analysis including Fefferman's invariant theory, the Chern-Moser theory, the Cheng-Yau solution of Kahler-Einstein metrics, to provide an affirmative solution of a conjecture posed by Cheng-Yau. The conjecture stated that the Bergman metric of a bounded strongly pseudoconvex domain is Einstein if and only if the domain is holomorphically equivalent to the ball.