The present paper reviews our research in the field of NO + H-2 reactions over Pt, Rh, 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 and spatio-temporal pattern formation. No oscillations in rate have been observed over Pd(1 1 1) and Ru(0 0 0 1). The rate oscillations over Pt, Rh and Ir can be divided into two groups: a Rh-like group which includes Rh(1 1 1)-like surfaces, Rh(1 1 0), Ir(1 1 0) and Ir(2 1 0) and a Pt-like group consisting of Pt(1 0 0), Ir(1 0 0) and lr(5 1 0). On the Rh-group surfaces 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 the Pt-group metal surfaces, 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 increases.