Synthesis and characterization of Ge based nanostructures are presented. Ion beam synthesis of pure Ge nanocrystals by ⁷⁴Ge⁺ implantation into a silica matrix is presented and the strategy to narrow the size distribution by controlling the substrate temperature during implantation is discussed. The size distribution of the sputter synthesized Ge nanocrystals is compared with that of ion beam synthesized Ge nanocrystals. Co-implantation of ⁷⁴Ge and ¹²⁰Sn forms binary eutectic alloy nanocrystals. The morphology of the nanocrystals is characterized with transmission electron microscopy and the thermodynamic implication of the equilibrium shape is discussed. It is demonstrated that nanocrystals with a metastable state can be formed with a single excimer laser pulse. The detailed structures and crystallinity of both equilibrium and metastable states are characterized using Raman spectroscopy, scanning transmission electron microscopy, and extended x-ray absorption fine structure spectroscopy. Initial composition dependent recovery of the equilibrium crystalline state upon heating of the metastable structure is investigated with ex-situ Raman spectroscopy and in-situ transmission electron microscopy equipped with a heating stage. The observed temperature tuning range extends from near room temperature to over 500°C depending on the Sn content, indicating metal mediated lowering of the crystallization temperature. The phase maps of each phase transformation step of the GeSn alloy nanocrystals are shown using energy filtered transmission electron microscopy, and the position shift of the bulk plasmon peak is demonstrated. One dimensional binary eutectic alloy nanostructures, GeAu nanowires, are also synthesized and characterized. In GeAu nanowires, composition dependent post-growth engineering produced various types of morphologies due to the effectively infinite length for atomic diffusion in one direction. The possibility of creating nanostructures with a combination of ion beam implantation and electron beam irradiation is visited and remaining issues are discussed.