An acute reduction in plasma osmolality causes rapid uptake of water by astrocytes but not by neurons, whereas both cell types swell as a consequence of lost blood flow (ischemia). Either hypoosmolality or ischemia can displace the brain downwards, potentially causing death. However, these disorders are fundamentally different at the cellular level. Astrocytes osmotically swell or shrink because they express functional water channels (aquaporins), whereas neurons lack functional aquaporins and thus maintain their volume. Yet both neurons and astrocytes immediately swell when blood flow to the brain is compromised (cytotoxic edema) as following stroke onset, sudden cardiac arrest, or traumatic brain injury. In each situation, neuronal swelling is the direct result of spreading depolarization (SD) generated when the ATP-dependent sodium/potassium ATPase (the Na+/K+ pump) is compromised. The simple, and incorrect, textbook explanation for neuronal swelling is that increased Na+ influx passively draws Cl− into the cell, with water following by osmosis via some unknown conduit. We first review the strong evidence that mammalian neurons resist volume change during acute osmotic stress. We then contrast this with their dramatic swelling during ischemia. Counter-intuitively, recent research argues that ischemic swelling of neurons is non-osmotic, involving ion/water cotransporters as well as at least one known amino acid water pump. While incompletely understood, these mechanisms argue against the dogma that neuronal swelling involves water uptake driven by an osmotic gradient with aquaporins as the conduit. Promoting clinical recovery from neuronal cytotoxic edema evoked by spreading depolarizations requires a far better understanding of molecular water pumps and ion/water cotransporters that act to rebalance water shifts during brain ischemia.