An important research field in Several Complex Variables and Complex Geometry is to understand the complete set of holomorphic invariants for an isolated complex singularity. There are two ways to approach this problem: The algebraic method is to investigate the ideals defining the singularity; and the analytic method is to study the Cauchy-Riemann links associated with the singularity. In this talk, we survey some of the recent work of the author with his coauthors on the studies of the complex structure of an isolated complex singularity through its local CR link. We will present examples and open problems, which may guide people for the future investigation along these lines of research.