Abstract—Molecular replication has branched into two parts, on one hand, it involves the non-informational copying of polymers which provides a replication environment indirectly, and on the other hand, the informational copying, including DNA or RNA replication, is a direct replication system. On account of the central dogma of molecular biology, after the transcription from DNA to mRNA, some living organisms require a specific RNA polymerase to catalyse and control the reaction of RNA self-replication. Based on the RNA world hypothesis, the self-replication of RNA at the earlier stage of the origin of life occurred under an enzyme-free condition. RNA replication process needs three steps: (a) separation of the duplex, (b) monomer extension of each strand, and (c) the end to end propagation of RNA strand. It was suggested that non-enzymatic RNA copying could take place in the presence of metal ions, like Mg2+ or Fe2+. Strand separation can be achieved by pH or temperature oscillation, and the RNA monomer extension could be attainable with the involvement of two activated nucleotides. This review gives a brief summary of the accomplishments scientists have made, and also concerns about several impediments in this process as well as their solutions.