Gamma-ray bursts (GRBs) are some of the most energetic explosions in the universe. They come from the core collapses of massive stars and the mergers of compact objects, and are observed as bright flashes of gamma rays (prompt emission) followed by long-lived, fading emission (afterglow) across the electromagnetic spectrum. The instruments on the Fermi Gamma-ray Space Telescope provide excellent observations of GRBs across a large energy range. The Gamma-ray Burst Monitor (GBM, 8 keV to 40 MeV) is currently the most prolific detector of GRBs, and the Large Area Telescope (LAT, ∼20 MeV to >300 GeV) has opened up the field of GRB observations to high-energy gamma rays. In this thesis, I present studies on improving the LAT’s capability to detect GRBs onboard in realtime, and analyses of both a single, extraordinary burst (the record-breaking GRB 130427A) and the population of GBM GRBs with precursors in their lightcurves. In a small fraction of GRBs, a dim peak appears before the much brighter peaks that are normally observed during the prompt emission. I explore whether the properties of GRBs with precursors suggests that precursors have a distinct physical origin from the rest of the prompt emission, and discuss the implications for models of GRB precursor emission.