The interaction of intense laser pulses with matter is giving rise to opportunities to investigate not only new physics but also to develop very compact accelerators and radiation sources. Advances in laser-plasma wake field accelerators (LWFAs) have now reached the point where they can be considered as drivers of compact radiation sources that cover a large spectral range. We present recent results from the Advanced Laser Plasma High-energy Accelerators towards X-rays (ALPHA-X) project at the University of Strathclyde. These include the production of high-brightness electron bunches with femtosecond durations and kilo-Ampère peak currents. We present new opportunities for harnessing laser-drive plasma waves to accelerate electrons to high energies and use these to drive ultra-compact radiation sources with unprecedented peak brilliance and pulse duration. We have demonstrated a brilliant table-top gamma ray source based on enhanced betatron emission in a plasma channel, which produces in excess of 109 photons per pulse in a spectral bandwidth of 10-20% stretching to beyond 7 MeV photon energies. We also present results of a compact synchrotron source based on a LWFA and undulator and discuss the potential of developing an ion-channel free-electron laser based on this technology.