Here we explore ways of transforming laser radiation into incoherent and coherent electromagnetic radiation using laserdriven 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 experimental 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 duration of a few femtoseconds. By extending the electron energy to 1 GeV, and for 1-2 fs duration pulses of 2 nm radiation peak powers of several MW per pC can be produced. The increased charge at higher electron energies will increase the peak power to GW levels, making the LWFA driven synchrotron an extremely useful source with a spectral range extending into the water window. With the reduction in size afforded by using LWFA driven radiation sources, and with the predicted advances in laser stability and repletion rate, ultra-short pulse radiation sources should become more affordable and widely used, which could change the way science is done.