DNA polymerases play a central role in biology by transferring genetic information from one generation to the next during cell division. Harnessing the power of these enzymes in the laboratory has fueled an increase in biomedical applications that involve the synthesis, amplification, and sequencing of DNA. However, the high substrate specificity exhibited by most naturally occurring DNA polymerases often precludes their use in practical applications that require modified substrates. Moving beyond natural genetic polymers requires sophisticated enzyme-engineering technologies that can be used to direct the evolution of engineered polymerases that function with tailor-made activities. Such efforts are expected to uniquely drive emerging applications in synthetic biology by enabling the synthesis, replication, and evolution of synthetic genetic polymers with new physicochemical properties.