Deep infrared images from the Hubble and Spitzer Space Telescopes have recently pushed the cosmic frontier back to just 500 million years after the Big Bang, delivering large samples of galaxies at redshifts 7<z<10. Deep rest-UV spectra have recently begun to complement these efforts, providing the first glimpse of the physical nature of early galaxies and revising our understanding of how Lyman-alpha escapes when the universe is mostly neutral. I will review the latest progress in characterizing the spectroscopic properties of z>7 galaxies and discuss implications for our understanding of early star formation and reionization.