This volume of Progress in Brain Research documents research presented at the 26th International Summer School of Brain Research (Amsterdam, Jun/Jul 2010) and looks at how the oscillations that characterize brain activity vary between task performance - the EEG power and performance modulations, rest - the MRI default mode and other networks, and sleep - the cortical slow oscillations. Studies over the past decade indicate that the study of these slow oscillations is essential for our understanding of plasticity, memory, brain structure from synapse to default mode network, cognition, consciousness and ultimately for our understanding of the mechanisms and functions of sleep and vigilance.