In situ transmission electron microscopy is used to obtain atom-resolved images of copper nanocrystals on different supports. These are catalysts for methanol synthesis and hydrocarbon conversion processes for fuel cells. The nanocrystals undergo dynamic reversible shape changes in response to changes in the gaseous environment. For zinc oxide-supported samples, the changes are caused both by adsorbate-induced changes in surface energies and by changes in the interfacial energy. For copper nanocrystals supported on silica, the support has negligible influence on the structure. Nanoparticle dynamics must be included in the description of catalytic and other properties of nanomaterials. In situ microscopy offers possibilities for obtaining the relevant atomic-scale insight.