The hydrogen-bonding recognition interactions of nucleobases are a fundamental property of nucleic acid chemistry and associated transcription, translation, and replication functions. Nucleobase interactions are central in protein biosynthesis, yielding sequence- and stereospecific macromolecules capable of assembly into precisely defined, complex shapes and morphologies that make up the machinery of life. As the understanding of nucleobases and their significance developed in the past century, chemists have inevitably sought to extend their function from a biological setting onto wholly synthetic platforms. Recent advances point to a burgeoning area of study which may soon bear fruit in some of the holy grails of polymer synthesis, namely sequence (and stereo) control, single chain manipulation, and controlled polymer folding. This Perspective seeks to summarize recent developments in the area of nucleobase containing polymers (including nucleobase mimics), with particular emphasis on controlled polymerization, self-assembly, and templating polymerization.