Chromatin is organized into higher-order structures that form subcompartments in interphase nuclei. Different categories of specialized enzymes act on chromatin and regulate its compaction and biophysical characteristics in response to physiological conditions. We present an overview of the function of chromatin structure and its dynamic changes in response to genotoxic stress, focusing on both subnuclear organization and the physical mobility of DNA. We review the requirements and mechanisms that cause chromatin relocation, enhanced mobility, and chromatin unfolding as a consequence of genotoxic lesions. An intriguing link has been established recently between enhanced chromatin dynamics and histone loss.