Abstract: During host infection, Toxoplasma gondii and related unicellular parasites move using gliding, which differs fundamentally from other known mechanisms of eukaryotic cell motility. Gliding is thought to be powered by a thin layer of flowing filamentous (F)-actin sandwiched between the plasma membrane and a myosin-covered inner membrane complex. How this surface actin layer drives the various gliding modes observed in experiments—helical, circular, twirling and patch, pendulum or rolling—is unclear. Here we suggest that F-actin flows arise through self-organization and develop a continuum model of emergent F-actin flow within the confines provided by Toxoplasma geometry. In the presence of F-actin turnover, our model predicts the emergence of a steady-state mode in which actin transport is largely directed rearward. Removing F-actin turnover leads to actin patches that recirculate up and down the cell, which we observe experimentally for drug-stabilized actin bundles in live Toxoplasma gondii parasites. These distinct self-organized actin states can account for observed gliding modes, illustrating how different forms of gliding motility can emerge as an intrinsic consequence of the self-organizing properties of F-actin flow in a confined geometry.