Under certain circumstances, decreasing the dimensions of a material may lead to elastic or anelastic properties that diverge from bulk behavior. A distinction is made between elastic deformation, for which bond rearrangements are not required, and anelastic behavior, which involves reversible deformation due to defect motion. Elastic deformation (due to bond stretching) remains structure-insensitive down to near-atomic length scales, and only small deviations are expected (of the order of 10%). More significant deviations can be observed in special cases, which are described in the article. However, elastic moduli that are much lower than expected are sometimes seen, even in careful experiments. It now appears that this behavior may be explainable by time-dependent anelastic relaxation mechanisms. In contrast to purely elastic behavior, anelastic behavior is very sensitive to microstructure and is found to be common and often significant when things become small.