The present paper reviews our research in the field of NO + H-2 reactions over Pt, Ph, Pd, Ir and Ru surfaces. Emphasis will be placed on the ability of these platinum group metals to produce oscillations in both reaction rate and selectivity, in addition to other non-linear processes such as hysteresis phenomena. In the case of Ph, non-linearity is related to periodic transitions between N- and O-rich surfaces, with O destabilising the N-adlayer and causing an acceleration in the N-2 production. However, in the case of Pt, the important step involves the creation of vacant sites required for NO dissociation, whereby products leaving the surface facilitate an autocatalytic rise in the concentration of such vacancies and, hence, reaction rate. Ir positions itself between the former two, because oscillations have been observed in two different regimes. Both a lower-temperature Pt-like and higher-temperature Rh-Like behaviours have been observed on different Ir surfaces. New results gained from field emission microscopy (FEM) and field ion microscopy (FIM) measurements are presented to consolidate the lower-temperature Pt-like behaviour, and confirm the dualistic nature of Ir. No oscillations in rate have been observed over Pd(111) or Ru(0001). The Ru surface exhibits selectivity to N-2 of almost 100% even in large excess of hydrogen.