In chemical reaction systems far from thermodynamical equlibrium rate oscil
lations and chemical wave patterns develop. This paper presents a condensed
overview of recent developments in the study of self-organization processe
s during heterogeneously catalyzed reactions, whereby the main emphasis is
focused on low pressure single crystal studies of oscillatory and pattern f
orming reactions on Pt and Rh surfaces. Chemical wave patterns on a macrosc
opic scale as well as reaction induced-microscopic roughening and coverage
fluctuations in nano-scale systems are discussed.