X-ray microscope has the property of providing high resolution. However, it should employ phase contrast for imaging materials consisting of light elements, such as biological samples, because the signal obtained from the penetrating X-rays is very weak and as a result the image contrast is extremely low with increasing photon energy and decreasing object size. Several phase contract methods for high-resolution X-ray microscope, including Zernike phase contrast mode, differential interference mode and off-axis holographic mode, are reviewed. Basic principles and main research progresses of these phase contrast microscopic techniques are presented, and their advantages and disadvantages are compared, in an attempt to show potential advantages as well as main challenges of X-ray phase contrast microscopic imaging techniques in detecting internal structures of biological samples.