Motivated by the general problem of moving topological defects in an otherwise ordered state and specifically, by the anomalous dynamics observed in vortex-antivortex annihilation and coarsening experiments in freely-suspended smectic-C films by Clark, et al., I study the deformation, energetics and dynamics of moving vortices in an overdamped xy-model and show that their properties are significantly and qualitatively modified by the motion.