We examine a number of distinct situations relating to heterogeneous catalysts where either a single atom (or ion), or a very small cluster of atoms functions as the locus of chemical turnover in various distinct kinds of conversion. There is little doubt that individual ions at certain crystallographic sites in nanoporous solids can indeed act as single-site catalysts. The situation concerning nanoclusters of pure metal (or bimetallic entities) is rather more ambiguous. What was hitherto thought to be an effective catalyst made up of a small cluster of Pt supported on γ-Al2O3 (for hydrogenation) now seems to be a single atom of Pt attached to a 5-coordinated AlIII ion. And in the case of Au or Pt on other supports, there is evidence that a single Pt atom, positively charged, but surrounded by alkali-metal ions, is a powerful catalyst for the water–gas shift (CO + H2O → H2 + CO2) reaction. We also report interesting results concerning the mobility of CeO2 support material.