Proteins have evolved as a variable platform that provides access to molecules with diverse shapes, sizes and functions. These features have inspired chemists for decades to seek artificial mimetics of proteins with improved or novel properties. Such work has focused primarily on small protein fragments, often isolated secondary structures; however, there has lately been a growing interest in the design of artificial molecules that mimic larger, more complex tertiary folds. In this Perspective, we define these agents as 'proteomimetics' and discuss the recent advances in the field. Proteomimetics can be divided into three categories: protein domains with side-chain functionality that alters the native linear-chain topology; protein domains in which the chemical composition of the polypeptide backbone has been partially altered; and protein-like folded architectures that are composed entirely of non-natural monomer units. We give an overview of these proteomimetic approaches and outline remaining challenges facing the field.