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X-ray imaging is of paramount importance for clinical and preclinical imaging but it is fundamentally restricted by the attenuation-based contrast mechanism, which has remained essentially the same since Roentgen's discovery a century ago. Different from the conventional method based on the attenuation contrast mechanism, X-ray phase-contrast imaging (XPCI) is proposed for the study of biological tissues and structures. This technique is also well suited for the imaging of materials such as carbon fibers, carbon composite materials, polymers, etc. This paper firstly discusses two XPCI methods. The first one is in-line phase contrast imaging based on the micro-focus X-ray source and the transport of intensity equation (TIE). The second one is the differential phase contrast imaging based on the grating and the normal X-ray source. Their imaging setups and the imaging principles are described. An experiment system based on the first XPCI method is set up. Phase contrast image of mosquito is acquired successfully. The first XPCI method has the simplest imaging setup but time-consuming. The second one has better X-ray utilization efficiency but the imaging layout is more complicated. Based on these work, a new micro-focus grating differential phase contrast imaging method is finally proposed and described.