The process of mass assembly in early galaxies and their transition into the Hubble sequence seen at later times are still poorly understood. Measurements of high-redshift galaxy kinematics and their star formation histories are crucial to trace early galaxy growth. With JWST/NIRSpec it is now possible to resolve galaxy stellar population and kinematic properties out to z~7, even for the low-mass and compact galaxies that form the progenitors of massive galaxies at lower redshifts. In this talk, I will discuss the new discoveries and challenges enabled by these data, and highlight the sophisticated modelling that is required to interpret the NIRSpec observations. I will show that typical star-forming galaxies at z~6 have highly diverse kinematic structures, and, surprisingly, the inferred kinematics and stellar populations indicate that these early galaxies may be dark matter dominated, pointing to a very early phase of stellar mass growth. Moreover, I will demonstrate that these JWST results appear in remarkably good agreement with cosmological simulations, which make clear predictions for the mass assembly histories of galaxies. Finally, I will turn to the massive end of the high-redshift galaxy population, and present first results from the RUBIES program, which suggest a very different evolutionary path for the most massive galaxies at z>5.
