Folding and self-assembly of biomacromolecules has inspired the development of discrete, non-natural oligomers that fold and/or self-assemble in a controlled manner. Though aromatic and aliphatic oligoamides remain unmatched for structural diversity and synthetic versatility, oligomers based on amide bond surrogates, such as urea backbones, also demonstrated a propensity for folding and self-assembly. In this Perspective, we review the advances in the design of oligomeric aromatic and aliphatic urea sequences (essentially N,N′-linked) that fold and/or self-assemble. Whenever applicable, the relationship between structure and function will be highlighted.