The three-dimensional (3D) architecture of a genome is non-random and known to facilitate the spatial colocalization of regulatory elements with the genes they regulate. Determining the 3D structure of a genome may therefore probe an essential step in characterizing how genes are regulated. Currently, there are several experimental and theoretical approaches that aim at determining the 3D structure of genomes and genomic domains; however, approaches integrating experiments and computation to identify the most likely 3D folding of a genome at medium to high resolutions have not been widely explored. Here, we review existing methodologies and propose that the integrative modeling platform (http://www.integrativemodeling.org), a computational package developed for structurally characterizing protein assemblies, could be used for integrating diverse experimental data towards the determination of the 3D architecture of genomic domains and entire genomes at unprecedented resolution. Our approach, through the visualization of looping interactions between distal regulatory elements, will allow for the characterization of global chromatin features and their relation to gene expression. We illustrate our work by outlining the recent determination of the 3D architecture of the α-globin domain in the human genome.