Renewed interest in the evolution of the ferroelectric phase transition temperature T (C) and the character of ordering of ferroelectric polarizations with finite size and shape is driven in part by several recent developments. An expanding array of pathways for producing nano-structured ferroelectric oxides with control of size, shape, and composition has emerged. Experimental characterization methods originally developed for thin films have been extended to ensemble-free investigations of functional properties of individual nanostructures. Progress in understanding the origin and nature of ferroelectric stability in ultra-thin films and nanostructures is reviewed. Specifically, we discuss evidence for a new surface adsorbate-driven mechanism for stabilizing ferroelectricity in nanostructures owing to a combination of recent proximal probe analysis and model calculation results, along with a new experimental paradigm for investigating and exploiting these effects and effects of finite curvature.