Lamins provide physical support to the nucleus and maintain nuclear shape. In many disease states linked to lamin and other nuclear envelope (NE) protein mutations, altered nuclear shape is viewed as a reflection of aberrant lamin and nuclear functions; however, there are also cell types with dramatically invaginated nuclei made with wild-type functional lamins. Closer inspection suggests four classes of NE invagination (NEI): large NE indentations or clefts, tubular NE invaginations that span from one side of the nucleus to the other, blind tubular NE invaginations that project variable distances into the nucleus, and blind invaginations of the inner nuclear membrane alone. These NEIs are likely formed by a combination of NE interactions with the cytoskeleton and with chromatin. Specific functions of NEIs are still being investigated, but their increasing relative nuclear surface area could increase NE/lamin functions in genome organization and regulation. Indeed, NEIs have recently been shown to hold a unique epigenetic signature compared to other NE regions in the same cell. Furthermore, studies have shown that tubular NEIs contain a Ca2+ store and that each NEI demarcates a cytoplasmic nanocourse, where calcium appears to be exchanged across the ONM between the NEI lumen and thus isolated cytoplasmic nanocourses. Therefore, Ca2+ flux at NEIs could additionally provide a more direct/rapid route to genome regulation compared to traditional signalling cascades. Here we discuss what is currently known about NEIs and the various possibilities of how they may contribute to genome regulation.