Chromatin encapsulates not only genomic sequence information but also its structural organization. Chromosome folding patterns may juxtapose distal functional elements of DNA in space and are thought to regulate gene expression. Directly visualizing chromosome architecture to study this grammar of chromosome folding has been but a longstanding ambition in the field of epigenetics. An emergent imaging technology called multiplexed DNA-FISH has made it possible to localize the positions of thousands of genomic loci with nanometer precision inside single cells. Given a cell’s ploidy, deriving chromatin conformations from this data initially assumed detecting a fixed number of bright signals and connecting them in sequential genomic order. But during cell cycle chromosomes copies are subject to change; it is also subject to copy number variations such as amplifications or deletions; it is subjected further still to technical noise such as false positives appearing as true signal, or signal dropout. In my thesis, I sought to develop a different framework that accounts for various sources of noise that have gone unappreciated in multiplexed DNA imaging, to show that by embracing the complexity of noise we can in fact uncover new biology previously unseen. First, I describe spatial genome alignment and its derivative polymer fiber karyotyping, methods for accurately resolving chromatin structures in a copy number agnostic fashion. We apply this method to multiplexed DNA-FISH data of mouse embryonic stem cells (mESC) and the mouse cortex. In dividing mESCs, we provide the first reconstructions of tightly intertwined sister chromatids decondensed in interphase – convoluted structures which previously could not be parsed by computer vision or by human eye. We go on to uncover unusual structures such as replicated homologs interacting in one single chromosome territory, suggestive of mitotic crossover. In the mouse cortex, we uncover tightly paired chromosomes in non-dividing neurons suggestive of sister chromatids in replication. Second, I summarize the field of spatial multi-omics, describing where spatial DNA imaging fits within the technological landscape, as well as describing other emerging technologies. I illustrate the principles of two main methods for achieving spatial resolution: imaging in situ and sequencing-based “release-and-capture” techniques, and further provide a broad survey of different multiplexing strategies for indexing cellular contents. I compare and contrast the two main families of spatial technologies, delineating how the distinct advantages of each lends them to different experimental applications. Given the new capabilities we and others uncovered using spatial multi-omics, such as detecting copy number variations and visualizing histone modifications, that extend beyond transcriptomic profiling, I provide a future perspective on how spatial multi-mics and the many channels of information it captures could inform future clinical applications.