Abstract: There is currently a growing interest in the realisation and optimization of hybrid plasma/catalyst systems for a multitude of applications, ranging from nanotechnology to environmental chemistry. In spite of this interest, there is, however, a lack in fundamental understanding of the underlying processes in such systems. While a lot of experimental research is already being carried out to gain this understanding, only recently the first simulations have appeared in the literature. In this contribution, an overview is presented on atomic scale simulations of plasma catalytic processes as carried out in our group. In particular, this contribution focusses on plasma-assisted catalyzed carbon nanostructure growth, and plasma catalysis for greenhouse gas conversion. Attention is paid to what can routinely be done, and where challenges persist.