In modern organisms, the hereditary material DNA encodes the instructions for the synthesis of proteins—the versatile nanomachines that enable modern cells to function and replicate. But how was this functional linkage between DNA and proteins established? According to the “RNA world” hypothesis, primordial living systems were based on self-replicating RNA molecules. Chemically speaking, RNA is closely related to DNA. However, in addition to storing information, RNA can fold into complex structures that have catalytic activity, similar to the protein nanomachines that catalyze chemical reactions in cells. These properties suggest that RNA molecules should be capable of catalyzing the replication of other RNA strands, and initiating self-sustaining evolutionary processes. Hence, RNA is of particular interest in the context of the origin of life as a promising candidate for the first functional biopolymer.