The replication of genetic information, as we know it from today's biology, relies on template-directed, polymerase-catalyzed extension of primers. It is known that short stretches of complementary RNA can form on templates in the absence of enzymes. This account summarizes recent work on efficient enzyme-free primer extension, both with 3'-amino-terminal deoxyribonucleotide primers and with primers made of unmodified RNA. Near-quantitative primer extension with half-life times on the order of hours has been demonstrated by using azaoxybenzotriazolides of nucleotides and downstream-binding oligomers. Further, small non-nucleosidic substituents placed on the terminus of the template or the downstream-binding oligomer have been shown to increase the rate and fidelity of primer-extension reactions. Since all four templating bases (A, C, G, T/U) direct sequence-selective primer-extension steps, we feel that there is renewed hope that full, nonenzymatic replication from monomers may eventually be achieved.