Here we explore ways of transforming laser radiation into incoherent and coherent electromagnetic radiation using laser- driven plasma waves. We present several examples based on the laser wakefield accelerator (LWFA) and show that the electron beam and radiation from the LWFA has several unique characteristics compared with conventional devices. We show that the energy spread can be much smaller than 1% at 130-150 MeV. This makes LWFAs useful tools for scientists undertaking time resolved probing of matter subject to stimuli. They also make excellent imaging tools. We present ex- perimental evidence that ultra-short XUV pulses, as short as 30 fs, are produced directly from an undulator driven by a LWFA, due to the electron bunches having a...