High intensity x-ray beams are used in a wide variety of applications in solid-state physics, medicine, biology and material sciences. Synchrotron radiation (SR) is currently the primary, high-quality x-ray source that satisfies both brilliance and tunability. The high cost, large size and low x-ray energies of SR facilities, however, are serious limitations. Alternatively, "novel" x-ray sources are now possible due to new small linear accelerator (LINAC) technology, such as improved beam emittance, low background, sub-Picosecond beam pulses, high beam stability and higher repetition rate. These sources all stem from processes that produce Radiation from relativistic Electron beams in (crystalline) Periodic Structures (REPS), or the periodic "structure" of laser light. REPS x-ray sources are serious candidates for bright, compact, portable, monochromatic, and tunable x-ray sources with varying degrees of polarization and coherence. Despite the discovery and early research into these sources over the past 25 years, these sources are still in their infancy. Experimental and theoretical research are still urgently needed to answer fundamental questions about the practical and ultimate limits of their brightness, mono-chromaticity etc. We present experimental results and theoretical comparisons for three exotic REPS sources. These are Laser-Compton Scattering (LCS), Channeling Radiation (CR) and Parametric X-Radiation (PXR).