The RNA world hypothesis states that during an early stage of life, RNA molecules functioned as genome and as the only genome-encoded catalyst. This hypothesis is supported by several lines of evidence, one of which is the in vitro selection of catalytic RNAs (ribozymes) in the laboratory for a wide range of reactions that might have been used by RNA world organisms. This review focuses on three types of ribozymes that could have been involved in the synthesis of RNA, the core activity in the self-replication of RNA world organisms. These ribozyme classes catalyze nucleoside synthesis, triphosphorylation, and the polymerization of nucleoside triphosphates. The strengths and weaknesses regarding each ribozyme's possible function in a self-replicating RNA network are described, together with the obstacles that need to be overcome before an RNA world organism can be generated in the laboratory.