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[en] This thesis investigates the use of high-power lasers for synchrotron radiation sources with high brilliance, from the EUV to the hard X-ray spectral range. Hereby lasers accelerate electrons by laser-wakefield acceleration (LWFA), act as optical undulators, or both. Experimental evidence shows for the first time that LWFA electron bunches are shorter than the driving laser and have a length scale comparable to the plasma wavelength. Furthermore, a first proof of principle experiment demonstrates that LWFA electrons can be exploited to generate undulator radiation. Building upon these experimental findings, as well as extensive numerical simulations of Thomson scattering, the theoretical foundations of a novel interaction geometry for laser-matter interaction are developed. This new method is very general and when tailored towards relativistically moving targets not being limited by the focusability (Rayleigh length) of the laser, while it does not require a waveguide. In a theoretical investigation of Thomson scattering, the optical analogue of undulator radiation, the limits of Thomson sources in scaling towards higher peak brilliances are highlighted. This leads to a novel method for generating brilliant, highly tunable X-ray sources, which is highly energy efficient by circumventing the laser Rayleigh limit through a novel traveling-wave Thomson scattering (TWTS) geometry. This new method suggests increases in X-ray photon yields of 2-3 orders of magnitudes using existing lasers and a way towards efficient, optical undulators to drive a free-electron laser. The results presented here extend far beyond the scope of this work. The possibility to use lasers as particle accelerators, as well as optical undulators, leads to very compact and energy efficient synchrotron sources. The resulting monoenergetic radiation of high brilliance in a range from extreme ultraviolet (EUV) to hard X-ray radiation is of fundamental importance for basic research, medical applications, material and life sciences and is going to significantly contribute to a new generation of radiation sources and free-electron lasers (FELs).