For decades proteins were thought to interact in a "lock and key" system, which led to the definition of a paradigm linking stable three-dimensional structure to biological function. As a consequence, any non-structured peptide was considered to be nonfunctional and to evolve neutrally. Surprisingly, the most commonly shared peptides between eukaryotic proteomes are low-complexity sequences that in most conditions do not present a stable three-dimensional structure. However, because these sequences evolve rapidly and because the size variation of a few of them can have deleterious effects, low-complexity sequences have been suggested to be the target of selection. Here we review evidence that supports the idea that these simple sequences should not be considered just "junk" peptides and that selection drives the evolution of many of them.