Space-based slitless spectroscopy capabilities on-board the Hubble Space Telescope have made it possible for us to conduct spatially-resolved studies of star formation in high redshift galaxies for the first time. The future is truly slitless, with the James Webb Space Telescope and the Nancy Grace Roman Space Telescope vastly improving and capitalizing on the scientific gains we will make with this mode of observation. I will begin by demonstrating how spatially resolved studies with the Hubble Space Telescope have allowed us to determine which galaxy size growth mechanisms dominate and how the quiescent (not forming stars) population of galaxies builds up with redshift. Subsequently, I will unveil the first spatially resolved H-Alpha emission line maps of cluster galaxies at z~1 from the GCLASS survey, made possible with the Wide Field Camera 3 G141 grism on-board the Hubble Space Telescope, revealing what they have taught us about the shutdown of star formation in galaxy clusters at this crucial epoch in the history of cosmic star formation. I will end by presenting deep spatially resolved H-Alpha emission line maps of CANDELS galaxies at z~0.5 from the CLEAR survey, made possible with the Wide Field Camera 3 G102 grism on-board the Hubble Space Telescope, and what these have unveiled on galaxy size growth via star formation at intermediate redshifts. By synthesizing the few existing spatially-resolved studies of High-Redshift Galaxies between 0.5 < z < 1.7 we now have, I will provide the first results on how star formation propagates spatially in galaxies over time.