A modern understanding of how cerebral cortical lesions develop after acute brain injury is based on Aristides Leão's historic discoveries of spreading depression and asphyxial/anoxic depolarization. Treated as separate entities for decades, we now appreciate that these events define a continuum of spreading mass depolarizations, a concept that is central to understanding their pathologic effects. Within minutes of acute severe ischemia, the onset of persistent depolarization triggers the breakdown of ion homeostasis and development of cytotoxic edema. These persistent changes are diagnosed as diffusion restriction in magnetic resonance imaging and define the ischemic core. In delayed lesion growth, transient spreading depolarizations arise spontaneously in the ischemic penumbra and induce further persistent depolarization and excitotoxic damage, progressively expanding the ischemic core. The causal role of these waves in lesion development has been proven by real-time monitoring of electrophysiology, blood flow, and cytotoxic edema. The spreading depolarization continuum further applies to other models of acute cortical lesions, suggesting that it is a universal principle of cortical lesion development. These pathophysiologic concepts establish a working hypothesis for translation to human disease, where complex patterns of depolarizations are observed in acute brain injury and appear to mediate and signal ongoing secondary damage.