Tandem repeats occur in 14% of all proteins. The repeat unit lengths range from a single amino acid to more than 100 residues and the repeat number is sometimes over 100. Understanding the structures, functions, and evolution of these repeats is a significant goal in both proteomics and genomics. This review summarizes experimental studies addressing structural features of tandem repeats of short oligopeptides that are rich in proline, glycine, asparagine, serine, and/or threonine. The oligopetides include (PGMG) and (PNN) in biomineralization protein (PM27), and (NPNA) in Plasmodium falciparum circumsporozoite protein, (YSPTSPS) in RNA polymerase II, (PHGGGWGQ) in the prion protein, (YGHGGG(N)) and (YNHGGG(G)) in plant glycine-rich proteins, (PGQGQQ), (PGQGQQGQQ) and (GYYPTSOQQ) of wheat HMW glutenin, (FGGMGGGKGG) in Aequipecten abductin. Spectroscopic studies including NMR and CD indicate that these peptides adopt type I and II β-turns, polyproline II helices, loop conformations, and random coils. Formation of these structures frequently depends on pH, solvent, temperature and hydration. The loop conformations are sometimes stabilized by cation-π, CH-π, and/or amino-aromatic interactions. These observations indicate that many tandem repeats are largely flexible. In addition to generating repeating domains and providing flexible linkers between domains, the tandem repeats of (PHGGGWGQ), (YGHGGG(N)) and (YNHGGG(G)) and those in titin bind Cu ions; whereas, tandem repeats of (NPNA) and those in elastin bind Ca ions. The interactions of some tandem repeats with various target proteins probably involve an induced fit. The tandem repeats in tropoelastin, flagelliform silk, wheat HMW glutenin, abductin, titin, and human nucleoporin, nup153, are responsible for elastomeric properties.