The cell needs to stably maintain its genome and protect it from uncontrolled modifications that would compromise its function. At the same time, the genome has to be a plastic structure that can dynamically (re)organize to allow the cell to adopt different functional states. These dynamics occur on the nanometer to micrometer length scale, i.e. ranging from the level of single proteins up to that of whole chromosomes, and on a microsecond to hour time scale. Here, we review different contributions to the dynamic features of the genome, describe how they are determined experimentally, and discuss the results of these measurements in terms of how the requirements for stability and plasticity are accommodated with specific activities in the nucleus.