To fully understand the properties of functional nanostructures such as catalytic nanoclusters, it is necessary to know the positions of all the atoms in the nanostructure. The catalytic properties of metal nanoclusters can often be improved by the addition of a second metal, but little is known about the role of the different metals in these bimetallic catalysts, or about their interactions with each other and the support material. Here we show that aberration-corrected scanning transmission electron microscopy of supported rhodium-iridium clusters, combined with dynamic multislice image simulations, can identify individual atoms, map the full structure, and determine changes in the positions of metal atoms in sequential images. This approach could help in the development of new and improved catalysts and other functional nanostructures.