Understanding when and how the first galaxies formed and what sources reionized the universe are key goals of extragalactic astronomy. Thanks to deep surveys with the powerful WFC3/IR camera on the HST, the observational frontier of galaxy build-up now lies at only ~450 Myr after the Big Bang, at redshifts z ~10-12. In combination with deep data from Spitzer/IRAC we can now probe the evolution of the stellar mass density over 96% of cosmic history. However, detecting and characterizing galaxies at these early epochs is challenging even for HST and the sample sizes at the earliest redshifts are still very small. The Hubble Frontier Fields provide a prime new dataset to improve upon our current, sparse sampling of the UV luminosity function at z>8 from blank fields to answer some of the most pressing open questions. For instance, even the evolution of the cosmic star-formation rate density at z>8 is still debated. While our measurements based on blank field data indicate that galaxies with SFR>0.7 Msol/yr disappear quickly from the cosmic record between z~8 and z~10, other previous results, e.g., from the CLASH survey favor a more moderate decline. Here, we briefly review the recent progress in studying galaxy build-up out to z~10 from the combined blank field and existing Frontier Field datasets and discuss their implications for primordial galaxy formation and cosmic reionization.