The neurophysiology of non-rapid eye movement sleep is characterized by the occurrence of neural network oscillations with distinct origins and frequencies, which act in concert to support sleep-dependent information processing. Thalamocortical circuits generate slow (0.25–4 Hz) oscillations reflecting synchronized temporal windows of cortical activity, whereas concurrent waxing and waning spindle oscillations (8–15 Hz) act to facilitate cortical plasticity. Meanwhile, fast (140–200 Hz) and brief (< 200 ms) hippocampal ripple oscillations are associated with the reactivation of neural assemblies recruited during prior wakefulness. The extent of the forebrain areas engaged by these oscillations, and the variety of cellular and synaptic mechanisms involved, make them sensitive assays of distributed network function. Each of these three oscillations makes crucial contributions to the offline memory consolidation processes supported by non-rapid eye movement sleep. Slow, spindle and ripple oscillations are therefore potential surrogates of cognitive function and may be used as diagnostic measures in a range of brain diseases. We review the evidence for disrupted slow, spindle and ripple oscillations in schizophrenia, linking pathophysiological mechanisms to the functional impact of these neurophysiological changes and drawing links with the cognitive symptoms that accompany this condition. Finally, we discuss potential therapies that may normalize the coordinated activity of these three oscillations in order to restore healthy cognitive function.