Chromosome conformation capture techniques are producing a huge amount of data about the architecture of our genome. These data can provide us with a better understanding of the events that induce critical regulations of the cellular function from small changes in the three-dimensional genome architecture. Generating a unified view of spatial, temporal, genetic and epigenetic properties poses various challenges of data analysis, visualization, integration and mining, as well as of high performance computing and big data management. Here, we describe the critical issues of this new branch of bioinformatics, oriented at the comprehension of the three-dimensional genome architecture, which we call Nucleome Bioinformatics, looking beyond the currently available tools and methods, and highlight yet unaddressed challenges and the potential approaches that could be applied for tackling them. Our review provides a map for researchers interested in using computer science for studying Nucleome Bioinformatics, to achieve a better understanding of the biological processes that occur inside the nucleus.