||Recently, One-dimensional nanostructures such as nanowires, nanograting, and nanotrenches, have attracted great attention due to their important applications in nano science and technology. They are expected to play indispensible roles in the development of innovative nano-scale electronic, optoelectronic and spintronic devices. The binary chalcogenide semiconductors, including ZnSe, ZnO, BixTey and NixSey etc, are expected to have unique photoelectric, thermoelectric or spintronic properties in the nanoscale, which makes them among the most popular materials used to fabricate 1D nanostructures. In this study, the fabrication and characterization of a number of 1D chalcogenide nanostructures grown by the molecular beam epitaxy (MBE) technique will be discussed. The highly aligned nanotrenches and nanograting with narrow width below 30nm were fabricated on the ZnSe (100) surfaces using in-situ metal-catalyzed self assembly methods. The orientation, geometry and formation mechanisms of these 1D surface nanostructures were studied through detailed microstructural characterizations. The nanotrenches were found to be induced by mobile AuZnδ nanoparticles through catalyzed decomposition of ZnSe along one specific anti-parallel pair of the <110> direction family. The ZnSe nanograting with the same orientation as that of the nanotrenches, was found to result from an Fe-Se exchange interaction and selective surface decomposition of ZnSe. The unique reflection high energy electron diffraction (RHEED) patterns resulted from the nanograting was fully understood using a model based on Ewald construction. Two types of binary chalcogenide nanowires, the bismuth telluride nanowires and the Ni3Se4/ZnSe heterostructured nanowires, were also synthesized and studied in this study. The synthesis of bismuth telluride nanowires was achieved using Au-nanoparticles assisted self assembly or vapor-solid-solid (VSS) mechanism. The activation of these two mechanisms was studied, which was found to depend on the density of the Au nanoparticles. To optimize the synthesis of bismuth telluride nanostructures, an effective approach using the ZnSe nanowires as the seeds was demonstrated. The Ni3Se4/ZnSe heterostructured nanowires were grown by an innovative two-step VLS growth mode, which involves the growth of the top Au-catalyzed Ni3Se4 section and the growth of the bottom ZnSe section catalyzed by a hybrid catalyst consisting of the Au head and the top Ni3Se4 section. The underlying physics of the unusual ultra fast growth rate and the preferred orientations of the heterostructured nanowires were also addressed.