This paper reviews the progress in the VLBI (Very Long Baseline Interferometry) studies of Sgr A*, the best known supermassive black hole candidates with a dark mass concentration of 4x106 M⊙ at the center of the Milky Way. The emphasis is on the importance of the millimeter and sub-millimeter VLBI observations in the detection of Sgr A*'s intrinsic structure and search for the structural variation.