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The relationship between genotype and phenotype, or the fitness landscape, is the foundation of genetic engineering and evolution. However, mapping fitness landscapes poses a major technical challenge due to the amount of quantifiable data that is required. Catalytic RNA is a special topic in the study of fitness landscapes due to its relatively small sequence space combined with its importance in synthetic biology. The combination of in vitro selection and high-throughput sequencing has recently provided empirical maps of both complete and local RNA fitness landscapes, but the astronomical size of sequence space limits purely experimental investigations. Next steps are likely to involve data-driven interpolation and extrapolation over sequence space using various machine learning techniques. We discuss recent progress in understanding RNA fitness landscapes, particularly with respect to protocells and machine representations of RNA. The confluence of technical advances may significantly impact synthetic biology in the near future.