The specificity and predictability of hybridization make oligonucleotides a powerful platform to program assemblies and networks with logic-gated responses, an area of research which has grown into a field of its own. While the field has capitalized on the commercial availability of DNA oligomers with its four canonical nucleobases, there are opportunities to extend the capabilities of the hardware with unnatural nucleobases and other backbones. This Topical Review highlights nucleobases that favor hybridizations that are empowering for assemblies and networks as well as two chiral XNAs than enable orthogonal hybridization networks.