Heterogeneous media, such as micro-structured aqueous environments, could offer an alternative approach to the synthesis of biopolymers with novel functions. Structured media are here defined as specialized, self-assembled structures that are formed, e.g, by amphiphiles, such as liposomes, emulsion compartments and lipid-bilayer lattices. Another kind of media is represented by co-existing, self-assembled phases in the reaction medium, e.g., in water-ice matrices. These media have the capacity to assemble chemical molecules or complex catalytic assemblies into unique configurations that are unstable or unavailable in bulk aqueous phases. Reactions can then proceed which do not readily occur in homogeneous solutions. To gauge the potential of this idea, we have investigated the non-enzymatic polymerization of RNA from monomers in the presence of various catalysts.