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The authors discuss the 3-D and 2-D X-on-Y (XoY) assembly techniques, utilizing specific examples to illustrate the potential of these methods for the fabrication of high performance devices on arbitrary substrates. For fabrication of 3-D structures, a templated nanomaterial growth technique is used. Specifically, anodic aluminum oxide (AAO) is used as the growth template. Alternatively, for 2-D assembly, a nanomaterial transfer process is used, where the nanostructures are first grown on a convenient growth substrate, and then deterministically placed on a substrate of choice using photolithography in conjunction with a printing process. 2-D and 3-D XoY assembly and integration of nanostructured materials are demonstrated for electronics, sensing, and energy applications. The presented devices illustrate the versatility and potential of XoY techniques for the fabrication of a large array of high performance devices on flexible and low-cost substrates.