In site quantitative, high-contrast and high-resolution imaging of micro/nanoscale material is an important goal of the X-ray microscopy and imaging. A novel method which is called lensless imaging or coherent X-ray diffraction imaging, is a promising approach to solving these problems. In this review, a brief introduction to imaging theory and development of coherent X-ray diffraction imaging, and some typical applications in material science and biology are presented. For instance, two-dimensional (2D) imaging of Bi dopant distribution in a Si crystal, quantitative three-dimensional (3D) imaging of a GaN quantum dot with core shell structure, 2D imaging of stained Escherichia coli bacteria, nanoscale imaging and mechanisms of biomineralization of fish bones, 2D high-contrast imaging of an unstained herpes virus, 3D high-resolution imaging of an unstained yeast cell and in situ quantitative analysis are illuminated. Finally, the future prospect of coherent X-ray diffraction imaging is given. With the development of X-ray free electron lasers and combining cryogenic techniques with coherent X-ray diffraction microscopy, coherent diffraction imaging will be a powerful tool and widely used in materials science and biology.