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The notion of fitness landscapes, a map between genotype and fitness, was proposed more than 80 years ago. For most of this time data was only available for a few alleles, and thus we had only a restricted view of the whole fitness landscape. Recently, advances in genetics and molecular biology allow a more detailed view of them. Here we review experimental and theoretical studies of fitness landscapes of functional RNAs, especially aptamers and ribozymes. We find that RNA structures can be divided into critical structures, connecting structures, neutral structures and forbidden structures. Such characterisation, coupled with theoretical sequence-to-structure predictions, allows us to construct the whole fitness landscape. Fitness landscapes then can be used to study evolution, and in our case the development of the RNA world.