In the young universe, galaxies were blobby conglomerations of stars whose irregular structures were products of their dynamically violent environments.  Over time, star formation in these systems declined as the gas fraction dropped, and galaxies evolved into the spiral and elliptical structures with which we are familiar today.  I will review the early morphological evolution of galaxies during the first 6 Gyr of cosmic time and highlight advances in our understanding that have been uniquely enabled by studies of the internal kinematics of such distant galaxies and the role of large-scale gas flows in the galactic baryon cycle.  Such integral-field spectroscopy has recently proven a particular boon to efforts to develop a comprehensive picture of galaxy evolution, and I will discuss the promise of such technology (and the University of Toronto’s leading role therein) for scientific discovery in the coming decade.