In eukaryotic cells, the genome is organized in the form of chromatin composed of DNA and histones that organize and regulate gene expression. The dysregulation of chromatin remodeling, including the aberrant incorporation of histone variants and their consequent post-translational modifications, is prevalent across cancers. Additionally, nuclear envelope proteins are often deregulated in cancers, which impacts the 3D organization of the genome. Altered nuclear morphology, genome organization, and gene expression are defining features of cancers. With advances in single-cell sequencing, imaging technologies, and high-end data mining approaches, we are now at the forefront of designing appropriate small molecules to selectively inhibit the growth and proliferation of cancer cells in a genome- and epigenome-specific manner. Here, we review recent advances and the emerging significance of aberrations in nuclear envelope proteins, histone variants, and oncohistones in deregulating chromatin organization and gene expression in oncogenesis.