In this short review we present few selected sections of our own work on the catalytic reactions as studied on a nanoscale using the field emission and field ion microscopies (FEM/FIM) and the corresponding probe-hole techniques: magnetic field ion mass separation combined with the field ion appearance energy spectroscopy (FIAES) and an atom probe with a Wien-filter ion mass selection combined with the time of flight (ToF) and coincidence analyses. We focus on the CO respectively hydrogen oxidation on Pt nanofacets present on an apex of a Pt tip that serves as a model of a single catalytic pellet of a supported catalyst. Exhibiting a heterogeneous surface formed by different orientations, like a catalyst pellet, a Pt tip can be prepared and characterized with atomic resolution. Surface reactions in such a well-defined system can be monitored with a resolution of £ 2 nm by FEM or FIM and the reacting species originating from few selected surface sites can be analyzed by FIAES or ToF in a probe-hole experiment. By using the single tip the usual averaging of data over at least few catalytic pellets of the common array-type model catalyst is avoided and thus a ''smoothing out'' of the characteristics of the single particles can be eliminated. As a result, the correlation of processes on individual nanofacets and fluctuation effects can be studied in situ. Until now, the FIM/FEM techniques are known to be quite successful in studying the oscillating surface reactions on Pt and Rh surfaces. In the present review we concentrate, in turn, on the local reaction kinetics in the nanosized reaction systems as mirrored by spectroscopic measurements and on the fluctuation-induced deviations from the behaviour predicted by macroscopic rate laws.