Cosmic acceleration is one of the most surprising cosmological discoveries of the past century. Even the "simplest" explanations require new, cosmologically dominant energy components with exotic physical properties. Current and near-future experiments are seeking clues to the origin of cosmic acceleration by measuring the history of expansion and structure growth with sub-percent precision over a wide span of redshift. I will review the observational methods that underpin these measurements and assess the current state of play, with particular attention to recent measurements from the Dark Energy Spectroscopic Instrument (DESI) which suggest that the properties of dark energy are evolving at a startling rate. I will discuss the prospects and challenges for the new generation of experiments --- DESI, the Euclid mission, the Vera Rubin Observatory, and the Nancy Grace Roman Space Telescope --- which aim to sharpen cosmological measurements by a factor of ten.