This article is an edited transcript based on the David Turnbull Lecture given by EllenD. Williams of the University of Maryland on December 2, 2003, at the MaterialsResearch Society Fall Meeting in Boston. Williams received the award for "groundbreakingresearch on the atomic-scale science of surfaces and for leadership, writing, teaching,and outreach that convey her deep understanding of and enthusiasm for materialsresearch. This article focuses on the special properties of small structures that providemuch of the exciting potential of nanotechnology. One aspect of small structures-theirsusceptibility to thermal fluctuations-may create or necessitate new ways of exploitingnanostructures. The advent of scanned probe imaging techniques created newopportunities for observing and understanding such structural fluctuations and therelated evolution of nanostructure. Direct observations show that it is relatively easy forlarge numbers of atoms-the kinds of numbers that are present in nanoscale structures-to pick up and move about on the surface cooperatively with substantial impact on nanotomicron-scale structures. Such labile evolution of structure can be predictedquantitatively by using length-scale bridging techniques of statistical mechanics coupledwith scanned probe observations of structural and temporal distributions.The samemeasurements also provide direct information about the stochastic paths of structuralfluctuations that can be used outside of the traditional thermodynamic framework. Futurework involves moving beyond the classical thermodynamic picture to assess the impactthat the stochastic behavior has on the physical properties of individual nanostructures.