The eukaryotic cell nucleus displays a high degree of spatial organization, with discrete functional subcompartments that provide microenvironments where specialized processes take place. Concordantly, the genome also adopts defined conformations that, in part, enable specific genomic regions to interface with these functional centers. Yet the roles of many subcompartments and the genomic regions that contact them have not been explored fully. More fundamentally, it is not entirely clear how genome organization impacts function, and vice versa. The past decade has witnessed the development of a new breed of methods that are capable of assessing the spatial organization of the genome. These stand to further our understanding of the relationship between genome structure and function, and potentially assign function to various nuclear subcompartments. Here, we review the principal techniques used for analyzing genomic interactions, the functional insights they have afforded and discuss the outlook for future advances in nuclear structure and function dynamics.