For over 20 years, laboratories around the world have been applying the principles of Darwinian evolution to isolate DNA and RNA molecules with specific ligand-binding or catalytic activities. This area of synthetic biology, commonly referred to as in vitro genetics, is made possible by the availability of natural polymerases that can replicate genetic information in the laboratory. Moving beyond natural nucleic acids requires organic chemistry to synthesize unnatural analogues and polymerase engineering to create enzymes that recognize artificial substrates. Progress in both of these areas has led to the emerging field of synthetic genetics, which explores the structural and functional properties of synthetic genetic polymers by in vitro evolution. This review examines recent advances in the Darwinian evolution of artificial genetic polymers and their potential downstream applications in exobiology, molecular medicine, and synthetic biology.