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This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us have dug into these topics using the tools and the spirit of the statistical physics of disordered systems, and in particular the concept of a disordered (energy/fitness) landscape. After an introduction to RNA molecules and the perspectives they open not only in evolutionary and synthetic biology but also in medicine, we will introduce the important notions of energy and fitness landscapes for these molecules. In Section III we will review some models and algorithms for RNA sequence-to-secondary-structure mapping. Section IV discusses how the secondary-structure energy landscape can be derived from unzipping data. Section V deals with the inference of RNA structure from evolutionary sequence data sampled in different organisms. This will shift the focus from the `sequence-to-structure' mapping described in Section III to a `sequence-to-function' landscape that can be inferred from laboratory evolutionary data on DNA aptamers. Finally, in Section VI, we shall discuss the rich theoretical picture linking networks of interacting RNA molecules to the organization of robust, systemic regulatory programs. Along this path, we will therefore explore phenomena across multiple scales in space, number of molecules and time, showing how the biological complexity of the RNA world can be captured by the unifying concepts of statistical physics.