Owing to known genome sequences, modern strategies of DNA synthesis have made it possible to recreate in principle all known viruses independent of natural templates. We describe the first synthesis of a virus (poliovirus) in 2002 that was accomplished outside living cells. We comment on the reaction of laypeople and scientists to the work, which shaped the response to de novo syntheses of other viruses. We discuss those viruses that have been synthesized since 2002, among them viruses whose precise genome sequence had to be established by painstakingly stitching together pieces of sequence information, and viruses involved in zoonosis. Synthesizing viral genomes provides a powerful tool for studying gene function and the pathogenic potential of these organisms. It also allows modification of viral genomes to an extent hitherto unthinkable. Recoding of poliovirus and influenza virus to develop new vaccine candidates and refactoring the phage T7 DNA genome are discussed as examples.