We present a new cosmological, magnetohydrodynamical simulation for galaxy formation: TNG50, the third and final installment of the IllustrisTNG project. TNG50 evolves 2 × 2160 3 dark-matter particles and gas cells in a volume 50 comoving Mpc across. It hence reaches a numerical resolution typical of zoom-in simulations, with a baryonic element mass of 8.5 × 10 4 M and an average cell size of 70 − 140 parsecs in the star-forming regions of galaxies. Simultaneously, TNG50 samples ∼700 (6,500) galaxies with stellar masses above 10 10 (10 8 ) M at z = 1. Here we investigate the structural and kinematical evolution of starforming galaxies across cosmic time (0 z 6). We quantify their sizes, disk heights, 3D shapes, and degree of rotational vs. dispersion-supported motions as traced by rest-frame Vband light (i.e. roughly stellar mass) and by Hα light (i.e. star-forming and dense gas). The unprecedented resolution of TNG50 enables us to model galaxies with sub-kpc half-light radii and with 300-pc disk heights. Coupled with the large-volume statistics, we characterize a diverse, redshift-and mass-dependent structural and kinematical morphological mix of galaxies all the way to early epochs. Our model predicts that for star-forming galaxies the fraction of disk-like morphologies, based on 3D stellar shapes, increases with both cosmic time and galaxy stellar mass. Gas kinematics reveal that the vast majority of 10 9−11.5 M star-forming galaxies are rotationally-supported disks for most cosmic epochs (V rot /σ > 2 − 3, z 5), being dynamically hotter at earlier epochs (z 1.5). Despite large velocity dispersion at high redshift, cold and dense gas in galaxies predominantly arranges in disky or elongated shapes at all times and masses; these gaseous components exhibit rotationally-dominated motions far exceeding the collisionless stellar bodies. log M⋆ = 11.4 z = 2.0, ID 29443 3 kpc log M⋆ = 10.9 z = 2.0, ID 79350 3 kpc log M⋆ = 10.6 z = 2.0, ID 60750 3 kpc log M⋆ = 10.5 z = 2.0, ID 8069 3 kpc log M⋆ = 10.5 z = 2.0, ID 57099 3 kpc log M⋆ = 10.0 z = 2.0, ID 68178 3 kpc log M⋆ = 10.7 z = 2.0, ID 110543 3 kpc log M⋆ = 10.3 z = 2.0, ID 90627 3 kpc log M⋆ = 10.4 z = 2.0, ID 55107 3 kpc log M⋆ = 10.2 z = 2.0, ID 102285 3 kpc log M⋆ = 9.9 z = 2.0, ID 113349 3 kpc log M⋆ = 10.5 z = 2.0, ID 121252 3 kpc log M⋆ = 10.0 z = 2.0, ID 125841 3 kpc log M⋆ = 10.7 z = 2.0, ID 115247 3 kpc log M⋆ = 10.2 z = 2.0, ID 115582 3 kpc log M⋆ = 10.5 z = 2.0, ID 127580 3 kpc log M⋆ = 10.4 z = 2.0, ID 132290 3 kpc log M⋆ = 10.2 z = 2.0, ID 130665 3 kpc log M⋆ = 10.3 z = 2.0, ID 129661 3 kpc log M⋆ = 10.4 z = 2.0, ID 139177 3 kpc log M⋆ = 10.2 z = 2.0, ID 145492 3 kpc log M⋆ = 9.6 z = 2.0, ID 146306 3 kpc log M⋆ = 10.4 z = 2.0, ID 154635 3 kpc log M⋆ = 10.1 z = 2.0, ID 189521 3 kpc log M⋆ = 9.5 z = 2.0, ID 246343 Stellar Composite [jwst f200w, jwst f115w, jwst f070w] 3 kpc log M⋆ = 11.4 z = 2.0, ID 29443 3 kpc log M⋆ = 10.9 z = 2.0, ID 79350 3 kpc log M⋆ = 10.6 z = 2.0, ID 60750 3 kpc log M⋆ = 10.5 z = 2.0, ID 8069 3 kpc log M⋆ = 10.5 z = 2.0, ID 57099 3...