Thomson-scattering based x-ray radiation sources, in which a laser beam is scattered off a relativistic electron beam resulting in a high-energy x-ray beam, are currently being developed by several groups around the world to enable studies of dynamic material properties which require temporal resolution on the order of tens of femtoseconds to tens of picoseconds. These sources offer pulses that are shorter than available from synchrotrons, more tunable than available from so-called Ka sources, and more penetrating and more directly probing than ultrafast lasers. Furthermore, Thomson-scattering sources can scale directly up to x-ray energies in the few MeV range, providing peak brightnesses far exceeding any other sources in this regime. This dissertation presents the development effort of one such source at Lawrence Livermore National Laboratory, the Picosecond Laser-Electron InterAction for the Dynamic Evaluation of Structures (PLEIADES) project, designed to target energies from 30 keV to 200 keV, with a peak brightness on the order of 10{sup 18} photons {center_dot} s{sup -1} {center_dot} mm{sup -2} {center_dot} mrad{sup -2} {center_dot} 0.01% bandwidth{sup -1}. A 10 TW Ti:Sapphire based laser system provides the photons for the interaction, and a 100 MeV accelerator with a 1.6 cell S-Band photoinjector at the front end provides …