The 'non-linear' genome, or the spatial proximity of non-contiguous sequences, emerges as an important regulatory layer for genome organization and function, including transcriptional regulation. Here, we review recent genome-scale chromosome conformation mappings ('Hi-C') in developing and adult human and mouse brain. Neural differentiation is associated with widespread remodeling of the chromosomal contact map, reflecting dynamic changes in cell-type-specific gene expression programs, with a massive (estimated 20-50%) net loss of chromosomal contacts that is specific for the neuronal lineage. Hi-C datasets provided an unexpected link between locus-specific abnormal expansion of repeat sequences positioned at the boundaries of self-associating topological chromatin domains, and monogenic neurodevelopmental and neurodegenerative disease. Furthermore, integrative cell-type-specific Hi-C and transcriptomic analysis uncovered an expanded genomic risk space for sequences conferring liability for schizophrenia and other cognitive disease. We predict that spatial genome exploration will deliver radically new insights into the brain nucleome in health and disease.