Cluster science as a bridge linking atomic molecular physics and condensed matter inspired the nanomaterials development in the past decades,ranging from the single-atom catalysis to ligand-protected noble metal clusters.The corresponding studies not only have been restricted to the search for the geometrical structures of clusters,but also have promoted the development of cluster-assembled materials as the building blocks.The CALYPSO cluster prediction method combined with other computational techniques have significantly stimulated the development of the cluster-based nanomaterials.In this review,we will summarize some good cases of cluster structure by CALYPSO method,which have also been successfully identified by the photoelectron spectra experiments.Beginning with the alkali-metal clusters,which serve as benchmarks,a series of studies are performed on the size-dependent elemental clusters which possess relatively high stability and interesting chemical physical properties.Special attentions are paid to the boron-based clusters because of their promising applications.The NbSi12 and BeB16 clusters,for example,are two classic representatives of the silicon-and boron-based clusters,which can be viewed as building blocks of nanotubes and borophene.This review offers a detailed description of the structural evolutions and electronic properties of medium-sized pure and doped clusters,which will advance fundamental knowledge of cluster-based nanomaterials and provide valuable information for further theoretical and experimental studies.