From 2009 to 2014, the Baryon Oscillation Spectroscopic Survey (BOSS) used the SDSS telescope to obtain spectra of 1.5 million galaxies to get very accurate measurements of the Baryon Acoustic Oscillations (BAO) scale at redshift z ~0.5. At the same time, BOSS observed over 184 000 high redshift quasars (z>2.15) with the goal of detecting the BAO feature in the clustering of the intergalactic medium, using a technique known as the Lyman alpha forest (LyaF). In this talk I will overview the final results from the LyaF working group in BOSS, including the measurement of BAO at z=2.4 both from the auto-correlation of the LyaF (Bautista et al. 2017), and from its cross-correlation with quasars (du-Mas-des-Bourboux et al. 2017). From the combination of these studies we are able to measure the expansion rate of the Universe 11 billion years ago with a 2% uncertainty. Starting in 2020, the Dark Energy Spectroscopic Instrument (DESI) will increase this data set by an order of magnitude. DESI will provide an exquisite measurement of the expansion over cosmic time, while at the same time addressing other interesting questions: the sum of the mass of the neutrino species, properties of dark matter particles, tests of general relativity and the shape of the primordial power spectrum of density fluctuations.