Polymer sequence programmability is required for the diverse structures and complex properties that are achieved by native biological polymers, but efforts towards controlling the sequence of synthetic polymers are, by comparison, still in their infancy. Traditional polymers provide robust and chemically diverse materials, but synthetic control over their monomer sequences is limited. The modular and step-wise synthesis of peptoid polymers, on the other hand, allows for precise control over the monomer sequences, affording opportunities for these chains to fold into well-defined nanostructures. Hundreds of different side chains have been incorporated into peptoid polymers using efficient reaction chemistry, allowing for a seemingly infinite variety of possible synthetically accessible polymer sequences. Combinatorial discovery techniques have allowed the identification of functional polymers within large libraries of peptoids, and newly developed theoretical modeling tools specifically adapted for peptoids enable the future design of polymers with desired functions. Work towards controlling the three-dimensional structure of peptoids, from the conformation of the amide bond to the formation of protein-like tertiary structure, has and will continue to enable the construction of tunable and innovative nanomaterials that bridge the gap between natural and synthetic polymers.