Qβ phage replicase has been the first RNA-directed RNA polymerase purified to homogeneity and intensively studied in vitro. In the mid-sixties, papers on Qβ and related replicases appeared in nearly every issue of the PNAS journal. By 1968, the mechanism of its action seemed to be almost completely understood. However, even now, a half of century later, a number of fundamental questions remains unanswered. How does the replicase manage to prevent the template and its complementary copy from annealing during the entire replication round? How does it recognize its templates? What is the function of the translation factors present in the replicase molecule? What is the mechanism the replicase uses to join (recombine) separate RNA molecules? Even the determination of the crystal structure of Qβ replicase did not help much. Certainly, there remains a lot to discover in the replication of Qβ phage, one of the smallest viruses known.