Eukaryotic parasites have evolved striking biomechanical and morphogenetic abilities that (1) enable successful infection of billions of human bodies and (2) present an exciting frontier for biophysics. My work explores cellular dynamics, mechanobiology, and morphogenesis through key phenomena in the lives of parasites: motility, penetration of host tissue, and organismal shape change. This talk will focus on gliding motility, the unique form of cell locomotion used during host infection by unicellular apicomplexan parasites like Toxoplasma gondii and the Plasmodium species that cause malaria. Gliding is powered by a thin layer of flowing actin filaments at the parasite surface. How does the collective motion of surface actin filaments emerge, and how does it drive the varied parasite gliding movements that we observe experimentally? I will present findings based on single-molecule tracking of actin and myosin in Toxoplasma gondii parasites and develop a continuum model of emergent F-actin flow within the confines provided by Toxoplasma geometry. Our actin filament flocking model enables the exploration of distinct self-organized states tuned by filament lifetime, which can account for the diversity of observed Toxoplasma gliding motions. This theory-experiment interplay illustrates how different forms of gliding motility can arise as an intrinsic consequence of self-organized actin filament flows at a cell surface.