Particle accelerators have been revolutionizing discoveries in science, medicine, industry and national security for over a century. An estimated 30,000 particle accelerators are currently active around the world. In these machines, electromagnetic fields accelerate charged particles, such as electrons, protons, ions or positrons to velocities nearing the speed of light. Although their scientific appeal will remain evident for many decades, one limitation of the current generation of particle accelerators is their tremendous size, typically a mile long, and cost, which often limits access to the broader scientific community. Acceleration of electrons in plasmas, in particular in laser-driven plasmas, has been drawing considerable attention over the past decade. These laser wakefield accelerators promise to dramatically reduces the size of accelerators and revolutionize applications in medicine, industry, and basic sciences. Series: "Lawrence Livermore National Lab Science on Saturda...