The catalytic reaction concept was introduced in the growth of semiconductor micro- and nano-crystals. It was found that gallium nitride (GaN) micro- and nano-crystal structures, carbon nanaotubes, and silicon carbide (SiC) nanostructures could be efficiently grown using transition metal catalysts. The use of Ni catalyst enhanced the growth rate and crystallinity of GaN micro-crystals. At 1,100 ℃, the growth rate of GaN micro-crystals grown in the presence of Ni catalyst was over nine times higher than that in the absence of the catalyst. The crystal quality of the GaN microcrystals was almost comparable to that of bulk GaN. Good quality GaN nanowires was also grown over Ni catalyst loaded on Si wafer. The nanowires had 6H hexagonal structure and their diameter was in the range of 30-50 nm. Multiwall nanotubes (MWNTs) were grown over 20Fe : 20Ni : 60Al2O3 catalyst. However, single wall nanotubes (SWNTs) were grown over 15Co : 15Mo : 70MgO catalyst. This result showed that the structure of CNTs could be controlled by the selection of catalysts. The average diameters of MWNTs and SWNTs were 20 and 10 nm, respectively. SiC nanorod crystals were prepared by the reaction of catalytically grown CNTs with tetrametysilane. Structural and optical properties of the catalytically grown semiconductor micro- and nano-crystals were characterized using various analytic techniques.