Nanomaterials have long attracted extensive attention of researchers due to their various geometric shapes and unique physicochemical properties. The emerging bottom-up assembly methodology, which leverages weak interactions, provides an effective avenue to impart spatially oriented direction to nanoscale materials. DNA-mediated assembly stands out among these strategies because of the inherent specificity of the DNA materials, and has demonstrated to be an efficient means of engineering nanomaterials in a precise, hierarchical, and programmable way. The architectures constructed from the bottom up varying in basic units, dimensions, and configurations offer numerous opportunities for customizable and exotic performance in functional devices. Here, we concentrate on discussing the diversity of the bottom-up assembly reported over the past two decades with particular emphasis on DNA-mediated assembly, and highlight the structural complexity of the corresponding assemblies. Moreover, important advances achieved in properties of multidimensional assemblies constructed by nanomaterials are divided based on the categories and explored in detail. In addition, different types of nanomaterials that can serve as building blocks are also systematically reviewed here.