ConspectusNucleic acids are a distinct form of sequence-defined biopolymer. What sets them apart from other biopolymers such as polypeptides or polysaccharides is their unique capacity to encode, store, and propagate genetic information (molecular heredity). In nature, just two closely related nucleic acids, DNA and RNA, function as repositories and carriers of genetic information. They therefore are the molecular embodiment of biological information. This naturally leads to questions regarding the degree of variation from this seemingly ideal “Goldilocks” chemistry that would still be compatible with the fundamental property of molecular heredity.To address this question, chemists have created a panoply of synthetic nucleic acids comprising unnatural sugar ring congeners, backbone linkages, and nucleobases in order to establish the molecular parameters for encoding genetic information and its emergence at the origin of life. A deeper analysis of the potential of these synthetic genetic polymers for molecular heredity requires a means of replication and a determination of the fidelity of information transfer. While non-enzymatic synthesis is an increasingly powerful method, it currently remains restricted to short polymers. Here we discuss efforts toward establishing enzymatic synthesis, replication, and evolution of synthetic genetic polymers through the engineering of polymerase enzymes found in nature.To endow natural polymerases with the ability to efficiently utilize non-cognate nucleotide substrates, novel strategies for the screening and directed evolution of polymerase function have been realized. High throughput plate-based screens, phage display, and water-in-oil emulsion technology based methods have yielded a number of engineered polymerases, some of which can synthesize and reverse transcribe synthetic genetic polymers with good efficiency and fidelity.The inception of such polymerases demonstrates that, at a basic level at least, molecular heredity is not restricted to the natural nucleic acids DNA and RNA, but may be found in a large (if finite) number of synthetic genetic polymers. And it has opened up these novel sequence spaces for investigation. Although largely unexplored, first tentative forays have yielded ligands (aptamers) against a range of targets and several catalysts elaborated in a range of different chemistries. Finally, taking the lead from established DNA designs, simple polyhedron nanostructures have been described.We anticipate that further progress in this area will expand the range of synthetic genetic polymers that can be synthesized, replicated, and evolved providing access to a rich sequence, structure, and phenotypic space. “Synthetic genetics”, that is, the exploration of these spaces, will illuminate the chemical parameter range for en- and decoding information, 3D folding, and catalysis and yield novel ligands, catalysts, and nanostructures and devices for applications in biotechnology and medicine.