We fabricated two types of three-dimensional (3-D) nanoarchitectured current collectors consisting of one-dimensional (1-D) Cu/C core/sheath nanowires and two-dimensional (2-D) Cu/C core/sheath nanonets. High-capacity Ge nanoarrays were deposited onto the as-prepared Cu/C nanowires or Cu/C nanonets via thermal evaporation and a GeO2 removal process. The obtained samples have advantages over Li-ion battery anodes because of the highly porous ordered and aligned nanostructures. The Cu/C nanonet-based Ge anodes exhibited a large reversible capacity of 933mAhg−1 at a rate of 1C over 1000 cycles and an excellent rate capability of 1017mAhg−1 at a rate of 10C over 200 cycles. We demonstrated that the 3-D nanoarchitecture technology has significant advantages such as a long cycle life and high-rate capabilities for the anode design of Li-ion batteries during the Li–Ge alloying process.