More than twenty five years ago, a new method was proposed for the acceleration of electrons to high energies using lasers. The simplest implementation of a so-called laser wakefield accelerator involves sending an intense laser pulse through a gas to ionize it and form a plasma of dissociated electrons and ions. The radiation pressure of the laser pushes the plasma electrons aside, creating a density modulation, or 'wake.' This changing electron density can result in fields that accelerate particles thousands of times more strongly than in conventional machines, accelerating electrons to high energies in short distances. The compactness of these accelerators would allow higher energies for the frontiers of fundamental physics and make clinical and laboratory applications of accelerators practical. In work that brings the promise of laser-driven particle accelerators dramatically closer to reality, we have produced high-quality GeV electron beams in a plasma channel based accelerating structure akin to an optical fiber of only a few centimeters long. Recent progress will be presented, including the generation of intense THz and x-ray radiation. Applications for such accelerators as drivers for future light sources and high energy physics particle colliders will be described, including a discussion on the challenges in laser technology to drive these accelerators.