Tailoring the internal structure and chemical composition of nanomaterials is an effective way to enhance their performance for a given application. Herein, we report a general wet-chemistry approach to produce copper (Cu)-based binary hollow nanostructures with well defined architectures and investigate their catalytic properties in electrochemical reactions. This strategy relies on the galvanic replacement between Cu seeds and noble metal precursors including ruthenium (Ru), rhodium (Rh), palladium (Pd), osmium (Os), iridium (Ir), and platinum (Pt) in oleylamine at an appropriate temperature, which is essential to balance the reduction kinetics of the noble metal precursors by oleylamine during their galvanic replacement with Cu seed particles. Typically, the bimetallic CuPt hollow nanostructures with polyhedral morphologies exhibit enhanced catalytic properties for the oxygen reduction reaction (ORR), while their spherical counterparts obtained at a relatively low temperature show high activity for the methanol oxidation reaction (MOR). In particular, we will also demonstrate a unique application of the CuRu hollow nanostructures in supercapacitors after converting them into binary metal oxides at elevated temperatures in air.