This Thesis describes the development of an electron-impact microfocus x-ray source and its application for phase-contrast imaging. The source is based on a novel, liquid-jet target concept. Stable and continuous operation can be achieved at substantially higher electron-beam power densities than conventional solid target based systems. The maximum x-ray brightness can potentially be increased by a factor of 10-1000, which would provide significantly improved performance in applications such as imaging. In order to reach the high x-ray brightness, comparable performance from the electron gun is needed. A LaB6-cathode-based electron gun is analyzed in terms of achievable e-beam brightness and beam quality and is found capable to deliver power densities in the 10-100 MW/mm2 range using optimized electro-optics. A proof-of-principle microfocus source has been developed. Experiments show that the liquid-metal-jet target can be operated at more than an order of magnitude higher e-beam power densities than modern solid-metal targets. This brightness enhancement has been utilized to acquire in-line phase-contrast images of weakly absorbing objects. The source potentially enables the application of high-resolution phase-contrast x-ray imaging with short exposure times in clinics and laboratories. Different liquid-jet-target materials have been tested. The Sn-jet (Ka=25.3 keV) could be suitable for mammography, whereas the Ga-jet ((Ka=9.2 keV) may be utilized for x-ray diffraction studies. In addition, a non-metallic methanol jet has been the demonstrated in stable x-ray operation. All materials and compounds found in liquid form can, thus, potentially be used for electron-impact liquid-jet-target x-ray generation. Scaling to higher e-beam power density and x-ray brightness levels is discussed and is determined to be feasible. Potential difficulties, such as debris emission and instabilities of the x-ray emission spot, are investigated in some detail. Larger and/or faster jets could overcome the present limitations because of their inherently higher heat load capacities. Dynamic-similarity experiments show that liquid jets can in principle be operated in a stable manner at much higher speeds than previously shown. / QC 20100915