Recent progress in the research of atomically-precise metal nanoclusters has identified a series of exceptionally stable nanoclusters with specific chemical compositions. Structural determination on such “magic size” nanoclusters revealed a variety of unique structures such as decahedron, icosahedron, as well as hexagonal close packing (hcp) and body-centered cubic (bcc) packing arrangements in gold nanoclusters, which are largely different from the face-centered cubic (fcc) structure in conventional gold nanoparticles. The characteristic geometrical structures enable the nanoclusters to exhibit interesting properties, and these properties are in close correlation with their atomic structures according to the recent studies. Experimental and theoretical analyses have been applied in the structural identification aiming to clarify the universal principle in the structural evolution of nanoclusters. In this mini-review, we summarize recent studies on periodic structural evolution of fcc-based gold nanoclusters protected by thiolates. A series of nanoclusters exhibit one-dimensional growth along the  direction in a layer-by-layer manner from Au28(TBBT)20 to Au36(TBBT)24, Au44(TBBT)28, and to Au52(TBBT)32 (TBBT: 4-tert-butylbenzenethiolate). The optical properties of these nanoclusters also evolve periodically based on steady-state and ultrafast spectroscopy. In addition, two-dimensional growth from Au44(TBBT)28 toward both  and  directions leads to the Au92(TBBT)44 nanocluster, and the recently reported Au52(PET)32 (PET: 2-phenylethanethiol) also follows this growth pattern with partial removal of the layer. Theoretical predictions of relevant fcc nanoclusters include Au60(SCH3)36, Au68(SCH3)40, Au76(SCH3)44, etc, for the continuation of 1D growth pattern, as well as Au68(SR)36 mediating the 2D growth pattern from Au44(TBBT)28 to Au92(TBBT)44. Overall, this mini-review provides guidelines on the rules of structural evolution of fcc gold nanoclusters based on 1D, 2D and 3D growth patterns.