After finishing the sequence of the human genome, a functional understanding of genome dynamics is the next major step on the agenda of the biosciences. New approaches, such as microarray techniques, and new methods of bioinformatics provide powerful tools aiming in this direction. In the last few years, important parts of genome organization and dynamics in a number of model organisms have been determined. However, an integrated view of gene regulation on a genomic scale is still lacking. Here, genome function is discussed from a complex dynamical systems perspective: which dynamical properties can a large genomic system exhibit in principle, given the local mechanisms governing the small subsystems that we know today? Models of artificial genetic networks are used to explore dynamical principles and possible emergent dynamical phenomena in networks of genetic switches. One observes evolution of robustness and dynamical self-organization in large networks of artificial regulators that are based on the dynamic mechanism of transcriptional regulators as observed in biological gene regulation. Possible biological observables and ways of experimental testing of global phenomena in genome function and dynamics are discussed. Models of artificial genetic networks provide a tool to address questions in genome dynamics and their evolution and allow simulation studies in evolutionary genomics.