RNA enzymes (ribozymes) often rely on specific base-pairing interactions to engage RNA substrates, which limits the substrate sequence generality of these enzymes. An RNA polymerase ribozyme that was previously optimized by directed evolution to operate in a more efficient and sequence-general manner can now recognize the RNA template, RNA primer, and incoming nucleoside 5'-triphosphate (NTP) entirely through tertiary interactions. As with proteinaceous polymerases, these tertiary interactions are largely agnostic to the sequence of the template, which is an essential property for the unconstrained transmission of genetic information. The polymerase ribozyme exhibits Michaelis-Menten saturation kinetics, with a catalytic rate of 0.1-1 min-1 and a Km of 0.1-1 μM. Earlier forms of the polymerase did not exhibit a saturable substrate binding site, but this property emerged over the course of directed evolution as the ribozyme underwent a structural rearrangement of its catalytic center. The optimized polymerase makes tertiary contacts with both the template and primer, including a critical interaction at the C2' position of the template nucleotide that opposes the 3'-terminal nucleotide of the primer. UV cross-linking studies paint a picture of how several portions of the ribozyme, including regions that were remodeled by directed evolution, come together to position the template, primer, and NTP within the active site for RNA polymerization.