Plasma waves excited by intense laser beams can be harnessed to produce femtosecond duration bunches of electrons with relativistic energies. The very large electrostatic forces of plasma density wakes trailing behind an intense laser pulse provide field potentials capable of accelerating charged particles to high energies over very short distances, as high as 1 GeV in a few millimetres. The short length scale of plasma waves provides a means of developing very compact high-energy accelerators, which could form the basis of compact next-generation light sources with unique properties. Tuneable X-ray radiation and particle pulses with durations of the order of or less than 5 fs should be possible and would be useful for probing matter on unprecedented time and spatial scales. If developed to fruition this revolutionary technology could reduce the size and cost of light sources by three orders of magnitude and, therefore, provide powerful new tools to a large scientific community. We will discuss how a laser-driven plasma wakefield accelerator can be used to produce radiation with unique characteristics over a very large spectral range.